CN106796279A - The geography of guiding surface ripple - Google Patents

Abstract

Various embodiments are disclosed for fixing a navigation position using guided surface waves emitted from guided surface wave waveguide probes at various ground stations. The navigation unit can fix its position by determining the travel time of the guided surface waves from the ground station to the navigation unit. In another embodiment, the navigation unit may also fix its position by determining changes in the strength of the guided surface waves after traveling from the ground station to the navigation unit. In other embodiments, the navigation unit may also fix its position by determining the phase difference of the phase-locked guided surface wave as it travels from the ground station to the navigation unit.

Description

The geography of guided surface waves

Cross References to Related Applications

This application claims benefit of and priority to co-pending U.S. Provisional Patent Application No. 62/049,039, filed September 11, 2014, entitled "GEOLOCATION WITH GUIDED SURFACEWAVES," and also claims The benefit and priority of U.S. Patent Application No. 14/839,175, filed on , is hereby incorporated by reference in its entirety.

This application is related to "Excitation and Use of Guided Surface Wave Modes on Lossy Media”, which is hereby incorporated by reference in its entirety. This application is also related to the application entitled "Excitation and Use of Guided Surface Wave Modes on Lossy Media”, which is hereby incorporated by reference in its entirety. This application is further related to co-pending U.S. Nonprovisional Patent Application, entitled "Excitation and Use of Guided Surface Wave Modes on Lossy Media," filed September 10, 2014 and assigned application number 14/483,089, which is adopted by All references are incorporated herein. This application is further related to co-pending U.S. Nonprovisional Patent Application entitled "Excitation and Use of Guided Surface Waves," filed June 2, 2015, and assigned Application Serial No. 14/728,507, which is incorporated by reference in its entirety in this. This application is further related to co-pending U.S. nonprovisional patent application entitled "Excitation and Use of Guided Surface Waves," filed June 2, 2015 and assigned application number 14/728,492, which is incorporated by reference in its entirety here.

Background technique

For nearly a hundred years, signals sent over radio waves have involved radiating fields launched using conventional antenna structures. Compared to radio science, electrical power distribution systems of the last century involve the transmission of energy guided along electrical conductors. An understanding of the difference between radio frequency (RF) and power transfer has existed since the early 1900's.

Contents of the invention

A system is disclosed comprising: a first guided surface waveguide probe comprising a first charging terminal raised above a first lossy conducting medium configured to generate at least one recombination field synthesized with a first charge terminal of the first lossy conducting medium a first wavefront (θ _i,B ) incident at a complex Brewster angle of incidence; circuitry coupled communicatively to said first guided surface waveguide probe, wherein circuitry coupled to said first guided surface waveguide probe is configured to via said first guided surface waveguide probe emits a first guided surface wave at least at a first frequency; a second guided surface waveguide probe comprising a second charging terminal raised on a second lossy conducting medium configured to generate at least one recombination field, which synthesizes a second wavefront at a second complex Brewster angle of incidence (θ _i,B ) of a second lossy conducting medium; circuitry communicatively coupled to said second guiding surface waveguide probe, wherein said communicatively coupled to The circuitry of the second guided surface waveguide probe is configured to transmit a second guided surface wave at least at a second frequency via the second guided surface waveguide probe; a third guided surface waveguide probe comprising a third guided surface waveguide probe raised a third charging terminal configured to generate at least one recombination field that synthesizes a third wavefront at a second complex Brewster incidence angle (θ _i,B ) of a third lossy conducting medium; and communicatively coupled circuitry to the third guided surface waveguide probe, wherein the circuitry communicatively coupled to the third guided surface waveguide probe is configured to transmit a third guided surface waveguide probe at least at a third frequency via the third guided surface waveguide probe surface waves. In some embodiments, the system further includes a first guided surface wave receiving structure configured to obtain electrical power from a first guided surface wave traveling along the ground medium and a second guided surface wave configured to obtain electrical power from a second guided surface wave traveling along the ground medium. obtaining electrical power from a second guided surface wave receiving structure, wherein the circuitry communicatively coupled to the second guided surface wave guide probe is also communicatively coupled to the first guided surface wave receiving structure, and the circuit is communicatively coupled to the The circuitry of the second guided surface waveguide probe is configured to at least: determine that the first guided surface wave is received by the first guided surface wave receiving structure; and respond to the first guided surface wave being received by the first guided surface wave a determination of reception by a guided surface wave receiving structure, transmitting said second guided surface wave at said second frequency via said second guided surface waveguide probe; circuitry communicatively coupled to a third guided surface waveguide probe further communicatively coupled to A second guided surface wave receiving structure, and circuitry communicatively coupled to a third guided surface waveguide probe configured to at least: determine that a first guided surface wave is received by said second guided surface wave receiving structure; and respond to said first guided surface wave receiving structure; A guided surface wave is received by the second guided surface wave receiving structure, and the third guided surface wave is transmitted at the third frequency via the third guided surface waveguide probe. In some embodiments of the system, the second guided surface wave is transmitted a predefined time period after the first guided surface wave is received by the first guided surface wave receiver. In some embodiments of the system, the third guided surface wave is transmitted a predefined time period after the first guided surface wave is received by the first guided surface wave receiver. In some embodiments of the system, at least one of the first guided surface wave, the second guided surface wave or the third guided surface wave includes a carrier wave for transmitting data. In some embodiments of the system, the data comprises a transmission packet comprising: a time stamp; and a position of at least one of the first guided surface wave waveguide probe, the second guided surface wave waveguide probe or the third guided surface wave waveguide probe . In some embodiments, the system further includes a feed network electrically coupled to the first charging terminal, the feed network providing a phase delay (Φ) matched to a wave tilt angle (Ψ) that is the same as that of the first guided surface waveguide probe Depends on the complex Brewster incidence angle (θ _i,B ) associated with the nearby lossy conducting medium.

A method is disclosed comprising transmitting a first guided surface wave at a first frequency via a first guided surface wave probe; transmitting a second guided surface wave at a second frequency via a second guided surface wave probe, wherein the second guided surface wave waves phase locked to the first guided surface wave; and transmitting a third guided surface wave at a third frequency via a third guided surface wave probe, wherein the third guided surface wave is phase locked to the first guided surface wave. In some embodiments of the method, the first frequency, the second frequency and the third frequency are harmonics of the fundamental frequency. In some embodiments of the method, the second frequency and the third frequency are harmonics of the first frequency. In some embodiments of the method, the first guided surface wave comprises a continuously generated wave. In some embodiments of the method, the second guided surface wave comprises a continuously generated wave. In some embodiments of the method, the third guided surface wave comprises continuously generated. In some embodiments of the method, at least one of the first guided surface wave, the second guided surface wave or the third guided surface wave is amplitude modulated to carry a transmission packet comprising an initial phase of the first guided surface wave.

An apparatus is disclosed, comprising: a guided surface wave receiving structure configured to obtain electrical power from a guided surface wave traveling along a ground medium; an electrical load coupled to the guided surface wave receiving structure, the electrical load being coupled to the a load at an excitation source of a guided surface wave waveguide probe generating said guided surface wave; a processor; a memory; and an application comprising a set of instructions stored in said memory which, when executed by said processor, The instructions cause the processor to: calculate the distance traveled by the guided surface wave from the guided surface wave waveguide probe to the location of the guided surface wave receiving structure; The distance traveled by the surface wave waveguide probe to the guided surface wave receiving structure determines a set of coordinates for the position. In some embodiments of the device, the guided surface wave receiving structure is selected from the group consisting of a linear probe, a tuned resonator and a coil. In some embodiments of the apparatus, the guided surface wave receiving structure is configured to receive the guided surface waves at a plurality of different frequencies substantially simultaneously. In some embodiments of the apparatus, causing the processor to calculate the distance traveled by the guided surface wave to the location of the apparatus further comprises causing the processor to at least: determine a guided surface wave corresponding to an initial intensity of the guided surface wave at the guided surface wave waveguide probe a first intensity of the surface wave; determining a second intensity of the guided surface wave corresponding to the intensity of the guided surface wave at the location of the device; calculating an intensity change between the first intensity and the second intensity ; and calculating the distance traveled by the guided surface wave based at least in part on the change in intensity. In some embodiments of the apparatus, causing the processor to calculate the distance traveled by the guided surface wave further comprises causing the processor to at least: determine the launch time of the guided surface wave from the guided surface wave waveguide probe; calculating a time difference between the launch time and the arrival time to generate a travel time of the guided surface wave; and calculating a distance traveled by the guided surface wave based at least in part on the travel time of the guided surface wave . In some embodiments, the emission times of the guided surface waves are encoded in the guided surface waves.

Other systems, methods, features and advantages of the present disclosure will be apparent to one with skill in the art upon examination of the following figures and detailed description. It is intended that all such additional systems, methods, features and advantages be included within this description, be within the scope of the present disclosure, and be protected by the accompanying claims.

Furthermore, all optional and preferred features and modifications of the described embodiments can be used in all aspects of the disclosure taught herein. Furthermore, the individual features of the dependent claims as well as all optional and preferred features and modifications of the described embodiments are combinable and interchangeable with each other.

Description of drawings

Many aspects of the disclosure can be better understood with reference to the following figures. The components in the figures are not necessarily to scale, emphasis instead may be placed in order to clearly illustrate the principles of the present disclosure. Also, in the figures, like reference numerals designate corresponding parts throughout the several figures.

FIG. 1 is a graph showing field strength as a function of distance for a guided electromagnetic field and a radiated electromagnetic field.

Figure 2 is a diagram illustrating a propagation interface with two regions employed for guiding the transmission of surface waves according to various embodiments of the present disclosure.

3 is a diagram illustrating a guided surface waveguide probe deployed for the propagation interface of FIG. 2 according to various embodiments of the present disclosure.

4 is a plot of examples of magnitudes of the approach and departure asymptotes of a first order Hankel function, according to various embodiments of the present disclosure.

5A and 5B are graphs illustrating complex angles of incidence of an electric field synthesized by a guided surface waveguide probe, according to various embodiments of the present disclosure.

6 is a graphical representation illustrating the effect of raising the charge terminal at locations where the electric field of FIG. 5A intersects a lossy conducting medium at Brewster's angle, according to various embodiments of the present disclosure.

7 is a graphical representation of an example of a guided surface waveguide probe according to various embodiments of the present disclosure.

8A-8C are graphical representations illustrating examples of equivalent image plane models of the guided surface waveguide probes of FIGS. 3 and 7 according to various embodiments of the present disclosure.

9A and 9B are graphical representations illustrating examples of single-wire transmission line and classical transmission line models of the equivalent image plane models of FIGS. 8B and 8C according to various embodiments of the present disclosure.

10 is a flow diagram illustrating an example of adapting the guided surface waveguide probe of FIGS. 3 and 7 to initiate guided surface waves along the surface of a lossy conducting medium, according to various embodiments of the present disclosure.

11 is a plot illustrating an example of a relationship between wave tilt angle and phase delay of the guided surface waveguide probes of FIGS. 3 and 7 according to various embodiments of the present disclosure.

12 is a diagram illustrating an example of a guided surface waveguide probe according to various embodiments of the present disclosure.

13 is a graphical representation illustrating incident resultant electric fields at complex Brewster angles to match guided surface waveguide modes at Hankel spanning distances, according to various embodiments of the present disclosure.

14 is a graphical representation of an example of the guided surface waveguide probe of FIG. 12 according to various embodiments of the present disclosure.

15A includes plots of examples of the imaginary and real parts of the phase delay (Φ _U ) of the charging terminal T1 of a guided surface waveguide probe according to various embodiments of the present disclosure.

15B is a schematic illustration of the guided surface waveguide probe of FIG. 14 according to various embodiments of the present disclosure.

FIG. 16 is a diagram illustrating an example of a guided surface waveguide probe according to various embodiments of the present disclosure.

17 is a graphical representation of an example of the guided surface waveguide probe of FIG. 16 according to various embodiments of the present disclosure.

18A to 18C illustrate examples of receiving structures that may be employed for receiving energy transmitted in the form of guided surface waves initiated by a guided surface waveguide probe, according to various embodiments of the present disclosure.

Figure 18D is a flowchart illustrating an example of adjusting a receiving structure according to various embodiments of the present disclosure.

19 illustrates an example of an additional receiving structure that may be employed to receive energy transmitted in the form of guided surface waves initiated by a guided surface waveguide probe, according to various embodiments of the present disclosure.

20A-E depict various circuit symbols used in the discussion of applications of guided surface waves for geolocation, according to various embodiments of the present disclosure.

21 is a schematic block diagram illustrating a navigation unit capable of determining its position based on guided surface waves emitted by one or more guided surface wave probes, according to various embodiments of the present disclosure.

FIG. 22 is a diagram illustrating positions of the navigation unit shown in FIG. 21 according to various embodiments of the present disclosure.

FIG. 23 is a diagram illustrating positions of the navigation unit shown in FIG. 21 according to various embodiments of the present disclosure.

24 is a schematic block diagram illustrating transmission packets sent from a ground station via guided surface waves according to various embodiments of the present disclosure.

FIG. 25 is a flowchart illustrating one example of functionality implemented as part of a multilateration application executed in the receiver shown in FIG. 21 according to various embodiments of the present disclosure.

26 is a flowchart illustrating one example of functionality implemented as part of a multilateration application executing in the receiver depicted in FIG. 21 according to various embodiments of the present disclosure.

27 is a flowchart illustrating one example of functionality implemented as part of a multilateration application executing in the receiver shown in FIG. 21 according to various embodiments of the present disclosure.

detailed description

To begin, some terminology should be established to provide clarity for subsequent discussions of concepts. First, as considered here, draw a formal distinction between radiating and directing electromagnetic fields.

As considered herein, radiated electromagnetic fields include electromagnetic energy emanating from a source structure in the form of waves that are not bound to a waveguide. For example, a radiated electromagnetic field is typically a field that leaves an electrical structure, such as an antenna, and propagates through the atmosphere or other medium, and is not bound to any waveguide structure. Once radiated electromagnetic waves leave an electrical structure such as an antenna, they continue to propagate in a propagation medium (such as air) independently of their source until they are dissipated, whether or not the source continues to operate. Once electromagnetic waves are radiated, they are not recoverable unless intercepted, and if not intercepted, the energy inherent in the radiated electromagnetic waves is lost forever. Electrical structures such as antennas are designed to radiate electromagnetic fields by maximizing the ratio of radiation resistance to structure loss resistance. Radiant energy is diffused and lost in space, whether or not a receiver is present. The energy density of the radiation field is a function of distance due to geometric divergence. Thus, the term "radiation" in all its forms as used herein refers to this form of electromagnetic propagation.

A guided electromagnetic field is a propagating electromagnetic wave whose energy is concentrated in or near a boundary between media with different electromagnetic properties. In this sense, a guided electromagnetic field is an electromagnetic field bound to a waveguide, and which can be characterized as being carried by an electric current flowing in the waveguide. If there is no load to receive and/or dissipate the energy transmitted in the guided electromagnetic wave, no energy is lost except for the energy dissipated in the conductivity of the guided medium. In other words, if there is no load for guiding electromagnetic waves, no energy is consumed. Thus, a generator or other source that produces a guided electromagnetic field delivers no real power unless a resistive load is present. For this reason, such generators or other sources run essentially idle until there is a load. This is similar to running a generator to generate 60 Hz electromagnetic waves sent through a power line with no electrical load. It should be noted that guiding an electromagnetic field or wave is equivalent to a so-called "transmission line mode". This is in contrast to radiated electromagnetic waves where actual power is always supplied to generate radiated waves. Unlike radiating electromagnetic waves, guided electromagnetic energy does not continue to propagate along a waveguide of finite length after the energy source is turned off. Accordingly, the term "guided" in all its forms as used herein refers to this transfer mode of electromagnetic propagation.

Referring now to FIG. 1 , there is shown a graph 100 of field strength in decibels (dB) above an arbitrary reference in volts per meter on a log-dB plot as a function of distance in kilometers , to further illustrate the difference between radiated and guided electromagnetic fields. Graph 100 of FIG. 1 shows a guided field strength curve 103 showing the field strength of the guided electromagnetic field as a function of distance. The guided field strength curve 103 is basically the same as the transmission line mode. Furthermore, the graph 100 of FIG. 1 shows a radiated field strength curve 106 which shows the field strength of the radiated electromagnetic field as a function of distance.

Of interest is the shape of the curves 103 and 106 for the guided wave and for the radiation propagation, respectively. The radiated field strength curve 106 falls geometrically (1/d, where d is distance), which is depicted as a straight line on a log-log scale. On the other hand, the guided field strength curve 103 has The characteristic decays exponentially and exhibits a distinct inflection point on the log-log scale109. The guided field strength curve 103 and the radiated field strength curve 106 intersect at a point 112, which occurs at a distance from the intersection. At distances less than the intersection distance at intersection point 112, the field strength of the guided electromagnetic field is substantially greater than the field strength of the radiated electromagnetic field at most locations. The opposite is true for distances greater than the intersection distance. Thus, the guided and radiated field strength curves 103 and 106 further illustrate the fundamental difference in propagation between the guided and radiated electromagnetic fields. For an informal discussion of the distinction between guided and radiated electromagnetic fields, see Milligan, T., Modern Antenna Design , McGraw-Hill, First Edition, 1985, pp. 8-9, which is fully incorporated herein by reference.

The distinction made above between radiating electromagnetic waves and guided electromagnetic waves is easily expressed formally and placed on a strict basis. Two such different solutions can emerge from the same linear partial differential equation, which is a wave equation, derived analytically from the boundary conditions imposed on the problem. The Green's function used in the wave equation itself includes a distinction between the nature of radiated and guided waves.

In empty space, the wave equation is a differential operator on a continuum whose eigenfunctions possess eigenvalues on the complex wavenumber plane. The transverse electromagnetic (TEM) fields are called radiation fields, and those propagating fields are called "Hertzian waves". However, in the presence of conducting boundaries, the wave equation plus boundary conditions mathematically leads to a spectral representation of the wavenumbers consisting of a continuous spectrum plus a sum of discrete spectra. For this, reference is made to Sommerfeld, A., "Uber die Ausbreitung der Wellen in der Drahtlosen Telegraphie", Annalen der Physik, Vol. 28, 1909, pp. 665-736. See also Sommerfeld, A., "Problems of Radio", published as Chapter 6 in Partial Differential Equations in Physics - Lectures on Theoretical Physics: Volume VI , Academic Press, 1949, pp. 236-289, 295-296; Collin, RE, "Hertzian Dipole Radiating Over a Lossy Earth or Sea: Some Early and Late 20th Century Controversies", IEEE Antennas and Propagation Magazine , Vol.46, No.2, April 2004, pp.64-79; and Reich, HJ , Ordnung, PF, Krauss, HL and Skalnik, JG, Microwave Theory and Techniques , Van Nostrand, 1953, pp. 291-293, each of which is fully incorporated herein by reference.

The terms "ground wave" and "surface wave" identify two distinct physical propagation phenomena. Surface waves arise analytically from distinct poles producing discrete components in the plane wave spectrum. See, eg, "The Excitation of Plane Surface Waves" by Cullen, AL, ( Proceedings of the IEE (British), Vol. 101, Part IV, August 1954, pp. 225-235). In this context, surface waves are considered guided surface waves. Surface waves (in the Zenneck-Sommerfeld guided wave sense) are physically and mathematically distinct from the now so familiar ground waves (in the Weyl-Norton-FCC sense) from radio broadcasting. These two propagation mechanisms result from the excitation of different types of eigenvalue spectra (continuous or discrete) on the complex plane. The field strength of guided surface waves decays exponentially with distance, as shown by curve 103 of Fig. 1 (more similar to propagation in lossy waveguides), and concentrates propagation in radial transmission lines, which is consistent with the classical Hertzian radiation of ground waves In contrast, ground waves propagate spherically, possess a continuum of eigenvalues, descend geometrically as shown in curve 106 of FIG. 1 , and come from branch-cut integration. For example by CR Burrows in "The Surface Wave in Radio Propagation over PlaneEarth" ( Proceedings of the IRE , Vol. 25, No 2, February 1937, pp. 219-229) and "The Surface Wave in Radio Transmission" ( Bell Laboratories Record , Vol.15, June 1937, pp.321-324), as demonstrated experimentally, the vertical antenna radiates ground waves without launching guided surface waves.

In summary, firstly, the continuous part of the spectrum of wavenumber eigenvalues corresponding to the branch-cut integral produces the radiation field, and secondly, the discrete spectrum with the corresponding residual sum emerging from the poles surrounded by the contour of the integral leads to Non-TEM migrating surface waves decaying exponentially in the direction of . This surface wave is a guided transmission line mode. For further illustration, reference is made to Friedman, B., Principles and Techniques of Applied Mathematics , Wiley, 1956, pp.pp.214, 283-286, 290, 298-300.

In free space, the antenna excites a continuous eigenvalue of the wave equation, which is the radiated field in which outwardly propagating RF energy with Ez and _Hφ in phase _is permanently lost. On the other hand, waveguide probes excite discrete eigenvalues, which cause transmission line propagation. See Collin, RE, Field Theory of Guided Waves , McGraw-Hill, 1960, pp. 453, 474-477. While this theoretical analysis has maintained the postulated possibility of initiating guided waves through a planar or spherical, open surface of a lossy homogeneous medium, no structure known in engineering has existed for more than a hundred years for any practical The efficiency to achieve this. Unfortunately, since it emerged in the early 20th century, the theoretical analysis presented above has largely remained theoretical, and there are no known structures for actually realizing guidance through a planar or spherical open surface of a lossy homogeneous medium The start of the wave.

According to various embodiments of the present disclosure, various guided surface waveguide probes are described that are configured to excite an electric field coupled into a guided surface waveguide mode along the surface of a lossy conducting medium. This guided electromagnetic field is substantially mode matched in magnitude and phase to the guided surface wave modes on the surface of the lossy conducting medium. Such guided surface wave modes may also be referred to as Zenneck waveguide modes. Due to the fact that the recombination field excited by the guided surface waveguide probe described here is substantially mode-matched to the guided surface waveguide mode on the surface of the lossy conducting medium, a guided wave in the form of a guided surface wave is initiated along the surface of the lossy conducting medium. electromagnetic field. According to one embodiment, the lossy conducting medium comprises a terrestrial medium such as the earth.

Referring to FIG. 2, there is shown a propagation interface prepared for examination of boundary value solutions to Maxwell's equations derived in 1907, which was described by Jonathan Zenneck in his paper Zenneck, J., "On the Propagation of Plane Electromagnetic Waves Along a Flat Conducting Surface and their Relation to Wireless Telegraphy", Annalen der Physik, Serial 4, Vol. 23, September 20, 1907, pp. 846-866. FIG. 2 shows cylindrical coordinates for propagating a wave radially along the interface between a lossy conducting medium as specified by region 1 and an insulator as specified by region 2 . Region 1 may for example comprise any lossy conducting medium. In one example, such lossy conducting media may include terrestrial media such as the earth or other media. Region 2 is a second medium that shares a boundary interface with Region 1 and has different compositional parameters relative to Region 1. Region 2 may for example comprise any insulator, such as the atmosphere or another medium. The reflection coefficient of such a boundary interface reaches zero only for incidence at complex Brewster angles. See Stratton, JA, Electromagnetic Theory , McGraw-Hill, 1941, p.516.

According to various embodiments, the present disclosure proposes various guided surface waveguide probes that generate an electromagnetic field substantially mode-matched to a guided surface waveguide mode on the surface of the lossy conducting medium comprising region 1 . According to various embodiments, this electromagnetic field essentially synthesizes wavefronts incident at complex Brewster angles of the lossy conducting medium that may result in zero reflections.

For further explanation, in region 2 where it is assumed that the ^ejωt field varies and where ρ≠0 and z≥0 (where z is the vertical coordinate perpendicular to the surface of region 1 and ρ is the radial dimension in cylindrical coordinates) , the closed-form exact solution of Zenneck's equations satisfying the boundary conditions along the interface is represented by the following electric and magnetic field components:

In region 1, where ^ejωt field variations are assumed and where ρ ≠ 0 and z ≤ 0, Zenneck's closed-form exact solution to Maxwell's equations satisfying the boundary conditions along the interface is represented by the following electric and magnetic field components:

In these expressions, z is the vertical coordinate perpendicular to the surface of region 1, and ρ is the radial coordinate, is the complex-argument Hankel function of the second kind and order n, u ₁ is the propagation constant in the positive vertical (z) direction in region 1, and u ₂ is the propagation constant in the vertical (z) direction in region 2 , σ1 is the conductivity of region ₁ , ω is equal to 2πf, where _f is the frequency of excitation, εo is the permittivity of free space, ε1 is the permittivity of region ₁ , A is the source constant imposed by the source, And γ is the surface wave radial propagation constant.

Propagation Constants in Directions The propagation constants in the ±z directions were determined by separating the wave equation above and below the interface between regions 1 and 2, and imposing boundary conditions. The practice is given in area 2:

and given in region 1,

u ₁ =−u ₂ (ε _r −jx). (8)

The radial propagation constant γ is given by:

It is a complex representation, where n is the complex index of refraction given by:

In all the above equations,

where ε _r includes the relative permittivity of region 1, σ ₁ is the conductivity of region 1, ε _o is the permittivity of free space, and μ _o includes the permeability of free space. Thus, the generated surface waves propagate parallel to the interface and decay exponentially perpendicular to the interface. This is known as evanescence.

Therefore, equations (1)-(3) can be viewed as cylindrically symmetric, radially propagating waveguide modes. See Barlow, HM, and Brown, J., Radio Surface Waves , Oxford University Press, 1962, pp. 10-12, 29-33. This disclosure details structures that excite this "open boundary" waveguide mode. In particular, according to various embodiments, the guiding surface waveguide probe is provided with a suitably sized charging terminal that is fed with voltage and/or current and positioned relative to the boundary interface between region 2 and region 1 . This can be better understood with reference to FIG. 3 , which shows a charge terminal T1 comprising _a charge terminal raised above a lossy conducting medium 203 along a vertical axis z perpendicular to the plane represented by the lossy conducting medium 203 (e.g., ground). An example of a guided surface waveguide probe 200a. The lossy conducting medium 203 constitutes region 1 , and the second dielectric 206 constitutes region 2 and shares a boundary interface with the lossy conducting medium 203 .

According to one embodiment, lossy conducting medium 203 may comprise a terrestrial medium such as planet Earth. To this end, such terrestrial medium includes all structures or forms, whether natural or man-made, subsumed thereon. For example, this terrestrial medium can include natural elements such as rocks, soil, sand, fresh water, sea water, trees, plants, and all other natural elements that make up our planet. Additionally, such terrestrial media may include man-made elements such as concrete, asphalt, building materials, and other man-made materials. In other embodiments, lossy conducting medium 203 may comprise some medium other than Earth, whether naturally occurring or man-made. In other embodiments, lossy conductive medium 203 may include other media such as man-made surfaces and structures, such as automobiles, airplanes, man-made materials such as plywood, plastic sheets, or other materials, or other media.

Where the lossy conducting medium 203 comprises a terrestrial medium or the earth, the second medium 206 may comprise the atmosphere above the ground. The atmosphere may thus be called the "atmospheric medium" comprising air and other elements that make up the atmosphere of the earth. Additionally, the second medium 206 may include other mediums relative to the lossy conducting medium 203 .

The guided surface waveguide probe 200a includes a feed network 209 that couples an excitation source 212 to a charging terminal T ₁ , for example via a vertical feed line conductor. According to various embodiments, charge Q1 is applied across charge terminal T1 to synthesize _an electric field based _on the voltage applied to terminal _T1 at any given moment. Depending on the angle of incidence (θ _i ) of the electric field (E), it is possible to substantially mode match the electric field to the guided surface waveguide modes on the surface of the lossy conducting medium 203 comprising region 1 .

By considering the Zenneck closed-form solutions of equations (1)–(6), the Leontovich impedance boundary condition between region 1 and region 2 can be stated as:

in is the cell vertical in the positive vertical (+z) direction, and is the magnetic field strength in region 2 expressed by equation (1) above. Equation (13) implies that the electric and magnetic fields specified in equations (1)–(3) can result in a radial surface current density along the boundary interface, where the radial surface current density can be specified by:

where A is a constant. Additionally, it should be noted that approaching the guided surface waveguide probe 200 (for ρ<<λ), the above equation (14) has the property:

The negative sign means that when the source current (I _o ) flows vertically upwards, as shown in Figure 3, the "going" ground current flows radially inward. By field matching on the "approach" of H _φ , it can be determined that:

Wherein in equations (1)-(6) and (14), q ₁ =C ₁ V ₁ . Therefore, the radial surface current density of equation (14) can be restated as:

The fields represented by equations (1)-(6) and (17) are of the nature of transmission line modes bound to lossy interfaces, not the radiation fields associated with ground wave propagation. See Barlow, HM and Brown, J., Radio Surface Waves , Oxford University Press, 1962, pp. 1-5.

In this regard, a review of the properties of the Hankel functions used in equations (1)-(6) and (17) is provided for these solutions of the wave equation. One can observe that the Hankel functions of the first and second kind and order n are defined as complex combinations of the standard Basel functions of the first and second kind:

These functions represent the radially inward and outward Propagated cylindrical waves. This definition is analogous to the relation e ^{± jx} = cos x ± j sin x. See, eg, Harrington, RF, Time-Harmonic Fields , McGraw-Hill, 1961, pp. 460-463.

Should is the output wave that can be identified from its large variable asymptotically linear state, and its large variable variable asymptotically linear state can be obtained directly from the series definitions of J _n (x) and N _n (x). Steering away from the surface waveguide probe:

When it is multiplied by e ^jωt , it has Spatially varying outwardly propagating cylindrical waves of the form e ^j(ωt-kρ) . The first order (n=1) solution can be determined by equation (20a) as

Approaching the guided surface waveguide probe (for ρ<<λ), the Hankel functions of the first and second kind are expressed as:

Note that these asymptotes represent complex quantities. When x is a real quantity, equations (20b) and (21) differ in phase by This corresponds to an additional phase advance or "phase boost" of 45°, or equivalently, λ/8. The approaching and departing asymptotes of the first order Hankel functions of the second kind have Hankel "intersecting" or transition points where they are of equal magnitude to that of the distance p ₌ Rx.

Thus, beyond the Hankel intersection point, the "far away" representation dominates with respect to the "approaching" representation of the Hankel function. The distance to the Hankel intersection point (or the Hankel intersection distance) can be found by equating equations (20b) and (21) for -jγρ, and solving for R _x . For x = σ/ωε _o , it can be seen that the asymptotes away from and towards the Hankel function are frequency dependent, with the Hankel intersection point moving outward as the frequency decreases. It should also be noted that the Hankel function asymptote also changes as the conductivity (σ) of the lossy conducting medium changes. For example, the electrical conductivity of soil can change as weather conditions change.

Referring to FIG. 4 , there is shown the first-order Hankel of equations (20b) and (21 ) for region 1 at an operating frequency of 1850 kHz, conductivity σ=0.010 mhos/m, and relative permittivity ε _r =15. Example of a plot of the magnitude of a function. Curve 115 is the magnitude away from the asymptote of equation (20b), and curve 118 is the magnitude of the approaching asymptote of equation (21), where the Hankel intersection occurs at a distance of Rx ₌ 54 feet Point 121. There is a phase shift between the two asymptotes at the Hankel intersection point 121 when the magnitudes are equal. It can also be seen that the Hankel crossing distance is much smaller than the wavelength of the operating frequency.

Considering the electric field components given by equations (2) and (3) for the Zenneck closed-form solution in region 2, it can be seen that the ratio of E _z and E _ρ turns asymptotically as:

where n is the complex index of Equation (10), and θ _i is the angle of incidence of the electric field. In addition, the vertical component of the mode-matched electric field of equation (3) turns asymptotically into:

It is linearly proportional to the free charge on the isolated component of the capacitance of the charging terminal rising at the terminal voltage, q _free =C _free ×V _T .

For example, the height H ₁ of the raised charging terminal T ₁ in FIG. 3 affects the amount of free charge on the charging terminal T ₁ . When the charging terminal T1 is near the ground plane of region ₁ , most of the charge Q1 _on the terminal is "bound". As charge terminal T ₁ rises, the bound charge decreases until charge terminal T ₁ reaches a height at which substantially all isolated charges are free.

The advantage _of the increased capacitive boosting of charge terminal T1 is that the charge _on the raised charge terminal T1 is further removed from the ground plane, resulting in an increased amount of free charge q _free coupling energy into guided surface waveguide modes. As the charge terminal T1 moves away from the ground plane, the charge distribution becomes more evenly distributed around the surface _of the terminal. The amount of free charge is related to the self _- capacitance of the charging terminal T1.

For example, the capacitance of a ball terminal can be expressed as a function of physical height above ground plane. The capacitance of a sphere at a physical height h above perfect ground is given by:

C _{elevated sphere} = 4πε _o a(1+M+M ² +M ³ +2M ⁴ +3M ⁵ +…), (24)

where the diameter of the ball is 2a, and where M=a/2h, h being the height of the ball terminal. As can be seen, the increase in terminal height h reduces the capacitance C of the charging terminal. It can be shown that for _a rise in charging terminal T1 at a height of about 4 times the diameter or greater (4D=8a), the charge distribution is approximately uniform around the spherical terminal, which can improve coupling into guided surface waveguide modes.

In the case of well-isolated terminals, the self-capacitance of a conductive ball can be approximated by C = _4πεo a, where a is the diameter of the ball in meters, and the self-capacitance of a disk can be approximated by C = _8εo a, where a is the radius of the disk in meters. Charging terminal T ₁ may comprise any shape, such as a sphere, disc, cylinder, cone, ring, cap, one or more rings, or any other random shape or combination of shapes. An equivalent ball diameter can be determined and used for the positioning of the charging terminal T ₁ .

This can further be understood with reference to the example of FIG. 3 , where the charging terminal T ₁ is raised at a physical height h _p =H ₁ above the lossy conducting medium 203 . To reduce the effect of "bonded" charges, charging terminal T1 may be located at _a physical height _of at least four times the spherical radius (or equivalent spherical radius) of charging terminal T1 to reduce the effect of bonded charge.

Referring next to FIG. 5A , a ray optics interpretation of the electric field generated by the raised charge Q ₁ on the charging terminal T ₁ of FIG. 3 is shown. As in optics, minimizing the reflection of the incident electric field can improve and/or maximize the energy coupling into the guided surface waveguide modes of the lossy conducting medium 203 . For an electric field (E _|| ) polarized parallel to the incident surface (not the boundary interface), the Fresnel reflection coefficient can be used to determine the reflection amount of the incident electric field, and the Fresnel reflection coefficient can be expressed as:

where _θi is the conventional angle of incidence measured against the surface normal.

In the example of Figure 5A, the optical interpretation of the rays shows parallel to the surface normal with Measure the incidence angle _θi of the incident plane polarized incident field. When Γ _|| (θ _i ) = 0 there will be no reflection of the incident electric field, and thus the incident electric field will be fully coupled into the guided surface waveguide mode along the surface of the lossy conducting medium 203 . It can be seen that the numerator of equation (25) becomes zero when the incident angle is as follows:

where x = σ/ωε _o . This complex angle of incidence (θ _i,B ) is called Brewster's angle. Referring back to equation (22), it can be seen that the same complex Brewster angle (θ _i,B ) relationship exists in both equations (22) and (26).

As shown in Figure 5A, the electric field vector E can be shown as an input non-uniform plane wave polarized parallel to the plane of incidence. The electric field vector E can be created from separate horizontal and vertical components as follows:

Geometrically, the illustration of Figure 5A proposes that the electric field vector E can be given by:

E _ρ (ρ,z)=E(ρ,z)cosθ _i , and (28a)

This means that the field ratio is:

A generalized parameter W called "wave tilt" is reported here as the ratio of the horizontal electric field component to the vertical electric field component and is given by:

It is complex and has both magnitude and phase. For electromagnetic waves in region 2, the wave tilt angle (Ψ) is equal to the angle between the normal to the wavefront at the boundary interface with region 1 and the tangent to the boundary interface. This can be seen more easily in Fig. 5B, which illustrates the isophase surfaces of electromagnetic waves and their normals to the radial cylindrically guided surface waves. At the boundary interface with a perfect conductor (z=0), the wavefront normal is parallel to the tangent to the boundary interface, resulting in W=0. However, in the case of lossy dielectrics, there is a wave tilt W because the wavefront normal is not parallel to the tangent to the boundary interface at z=0.

Applying equation (30b) to guided surface waves gives:

where the incident angle is equal to the complex Brewster angle (θ _i,B ), the Fresnel reflection coefficient of equation (25) disappears as shown in the following equation:

By adjusting the complex field ratio of equation (22), the incident field can be synthesized to be incident at complex angles where reflections are reduced or eliminated. establish this ratio as The resultant electric field is caused to be incident at complex Brewster angles so that the reflection disappears.

The concept of electrical effective height may provide further insight into synthesizing electric fields with complex angles of incidence using guided surface waveguide probes 200 . For a monopole with a physical height (or length) h _p (or length), the electrical effective height (h _eff ) has been defined as:

Since this expression depends on the magnitude and phase of the source distribution along the structure, the effective height (or length) is usually complex. The integration of the distribution current I( _z ) of the structure is performed over the physical height of the structure (hp ) and normalized to the ground current (I ₀ ) flowing upwards through the base (or input) of the structure. The distributed current along this structure can be expressed as:

I(z)=I _C cos(β ₀ z), (34)

where _β0 is the propagation factor of the current propagating on the structure. In the example of FIG. 3, _IC is the current distributed along the vertical structure guiding the surface waveguide probe 200a.

For example, consider a feed network 209 comprising a low loss coil (eg a helical coil) at the bottom of the structure and _a vertical feeder conductor connected between this coil and charging terminal T1. The phase delay due to the coil (or helical delay line) is θ _c = β _p l _C , where the physical length is l _C and the propagation factor is as follows:

where Vf is the _velocity factor on the structure, λ0 is the wavelength _at the supply frequency, and _λp is the propagation wavelength resulting from the _velocity factor Vf. The phase delay is measured with respect to the ground (pile) current I ₀ .

Additionally, the spatial phase delay along the length _lw of the vertical feedline conductor can be given by _θy = _{βw lw} , where _βw is the propagation phase constant for the vertical feedline conductor. In some implementations, the spatial phase delay can be approximated by _{θy = βwhp} because the difference between the physical height _hp of the guided surface waveguide probe 200a and the vertical feedline conductor length _lw is much smaller than the wavelength at the supply frequency (λ ₀ ). As a result, the total phase delay through the coil and the vertical feedline conductor is Φ = θ _c + θ _y , and the current fed from the bottom of the physical structure to the top of the coil is:

I _C (θ _c +θ _y )=I ₀ e ^jΦ , (36)

Among them, the total phase delay Φ is measured relative to the ground (pile) current I ₀ . Therefore, for the case of physical height h _p << λ ₀ , the electrical effective height of the guided surface waveguide probe 200 can be approximated by the following formula:

The complex effective height h _eff =h _p of the monopole at angle (or phase shift) Φ can be tuned such that the source field matches the wire surface waveguide mode and that guided surface waves are initiated on the lossy conducting medium 203 .

In the example of FIG. 5A , ray optics are used to illustrate the complex angle trigonometry of an incident electric field (E) with a complex Brewster angle of incidence (θ _i,B ) at a Hankel intersection distance (R _x ) 121 . Recall from equation (26) that for a lossy conducting medium, the Brewster's angle is complex and is specified by:

Electrically, the geometric parameter is related by the electrical effective height (h _eff ) of the charging terminal T1 by the following equation:

R _x tanψ _i,B = R _x × W = h _eff = h _p e ^jΦ , (39)

where ψ _i,B = (π/2) - θ _i,B is the Brewster's angle measured from the surface of the lossy conducting medium. For coupling into guided surface waveguide modes, the wave tilt of the electric field at the Hankel intersection distance can be expressed as the ratio of the electrical effective height to the Hankel intersection distance:

Since both the physical height (h _p ) and the Hankel intersection distance (R _x ) are real quantities, the angle (Ψ) of the required guided surface wave tilt at the Hankel intersection distance (R _x ) is equal to Phase (Φ) of the complex effective height (h _eff ). This implies that by varying the phase at the coil's supply point, and thus the phase shift in equation (37), the phase Φ of the complex effective height can be manipulated to match the wave tilt of the guided surface waveguide mode at the Hankel intersection point 121 Angle Ψ: Φ=Ψ.

In FIG. 5A , a right triangle _is shown having adjacent sides along the length Rx of the lossy conductive medium surface, and a ray 124 extending between the _Hankel intersection 121 at Rx and the center _of the charging terminal T1 and the complex Brewster angle ψ _i,B measured between the lossy conductive medium surface 127 between the Hankel intersection 121 and the charging terminal T ₁ . For a charging terminal T ₁ located at a physical height h _p and excited with a charge with an appropriate phase delay Φ, the resulting electric field is incident on this lossy conductive medium boundary interface at a Hankel intersection distance R _x , and at Brewster's angle . Under these conditions, guided surface waveguide modes can be excited with no or substantially negligible reflections.

If the physical height _of the charging terminal T1 is reduced without changing the phase shift Φ of the effective height (h _eff ), the resulting electric field intersects the lossy conducting medium 203 at the Brewster angle at a reduced distance from the guiding surface waveguide probe 200 . FIG. 6 graphically illustrates the effect of reducing the physical height of the charging terminal T ₁ on the distance of the incident electric field at Brewster's angle. As the height decreases from _h3 through h2 to _hi , the point where the electric field intersects the lossy conducting medium (eg, earth ₎ at Brewster's angle moves closer to the charging terminal location. However, as indicated by equation (39), the height H ₁ ( FIG. 3 ) of the charging terminal T ₁ should be equal to or higher than the physical height ( _hp ) in order to excite the distant component of the Hankel function. With the charging terminal T ₁ at or above the effective height (h _eff ), the lossy conductive medium 203 can be at or beyond the Hankel intersection distance (R _x ) 121 at Brewster's incidence angle (ψ _i,B =( π/2)-θ _i,B ) irradiation, as shown in Figure 5A. In order to reduce or minimize the bound charge _on the charging terminal T1, the height should be at least four times the spherical diameter (or equivalent spherical diameter) _of the charging terminal T1 as described above.

The guided surface waveguide probe 200 may be configured to establish an electric field with a wave tilt corresponding to a wave impinging the surface of the lossy conducting medium 203 at complex Brewster angles, thereby _by substantially mode matching to the Hank at (or beyond) Rx The guided surface wave modes at the intersection point 121 are used to excite radial surface currents.

Referring to FIG. 7 , a pictorial representation of an example of a guided surface waveguide probe 200b including charging terminal T ₁ is shown. An AC source 212 is used as _an excitation source for the charging terminal T1, which is coupled to the guided surface waveguide probe 200b through a feed network (Fig. 3) comprising a coil 215, such as a helical coil. In other implementations, AC source 212 may be inductively coupled to coil 215 through a primary coil. In some embodiments, an impedance matching network may be included to improve and/or maximize the coupling of AC source 212 to coil 215 .

As shown in FIG. 7, guided surface waveguide probe 200b may include _an upper charging terminal T1 (e.g., spherical at height hp) positioned substantially orthogonally by the lossy conducting medium along a vertical axis _z that is substantially Orthogonal to the plane represented by the lossy conducting medium 203 . The second medium 206 is located above the lossy conducting medium 203 . The charging terminal T ₁ has a self-capacitance C _T . During operation, _a charge Q1 is imposed _on terminal T1 depending _on the voltage applied to terminal T1 at any given moment.

In the example of FIG. 7 , coil 215 is coupled to ground stake 218 at a first end, and is coupled to charging terminal T ₁ via vertical feeder conductor 221 . In some implementations, the coil connection to charging terminal T ₁ may be adjusted using tap 224 of coil 215 as shown in FIG. 7 . The coil 215 may be energized by the AC source 212 at the operating frequency through a tap 227 on the lower portion of the coil 215 . In other implementations, AC source 212 may be inductively coupled to coil 215 through a primary coil.

The structure and adjustment of the guided surface waveguide probe 200 is based on various operating conditions, such as the transmission frequency, the condition of the lossy conducting medium (eg, soil conductivity σ and relative permittivity ε _r ), and the size of the charging terminal T ₁ . The refractive index can be calculated from equations (10) and (11) as follows:

where x=σ/ωε _o , and ω=2πf. The conductivity σ and the relative permittivity ε _r can be determined by test measurements of the lossy conducting medium 203 . The complex Brewster angle (θ _i,B ) measured from the surface normal can also be determined from equation (26) as follows:

Or measured from a surface as shown in Figure 5A as follows:

The wave tilt (W _Rx ) at the Hankel intersection distance can also be found using equation (40).

The Hankel intersection distance can also be found by equating the magnitudes of equations (20b) and (21) for -jγρ and solving for R _x as shown in FIG. 4 . The electrical effective height can then be determined from equation (39) using the Hankel intersection distance and the complex Brewster angle as follows:

h _eff = h _p e ^jΦ = R _x tanψ _i,B . (44)

As can be seen from equation (44), the complex effective height (h _eff ) includes the magnitude associated with the physical height (h _p ) of the charge terminal T ₁ , and the distance to intersect at Hankel (R _x ) The angle (Ψ) at which the wave is tilted at is associated with a phase delay (Φ). Using these variables and the selected charging terminal T1 configuration, it is possible to determine the configuration _of the guided surface waveguide probe 200 .

With charging terminal T ₁ at or above physical height (h _p ), feed network 209 ( FIG. ₃ ) and/or vertical feed lines connecting the feed network to charging terminal T ₁ can be adjusted to _The phase (Φ) of the charge Q1 matches the angle (Ψ) of the wave tilt (W). _The size of the charging terminal T1 may be chosen to provide _a sufficiently large surface area for the charge Q1 imposed on the terminal. _In general, it is desirable to make the charging terminal T1 as large as practical. _The size of the charging terminal T1 should be large enough to avoid ionization of the surrounding air, which could lead to discharges or sparks around the charging terminal.

The phase delay _θc of a helically wound coil can be determined from Maxwell's equations, as has been done by Corum, KL and JFCorum, "RF Coils, Helical Resonators and Voltage Magnification by CoherentSpatial Modes", Microwave Review , Vol.7, No.2, 2001 Discussed in September, pp. 36-45., which is fully incorporated herein by reference. For a helical coil with H/D > 1, the ratio of the velocity of propagation of waves (υ) to the speed of light (c) along the longitudinal axis of the coil, or "velocity factor", is given by:

where H is the axial length of the solenoid helix, D is the coil diameter, N is the number of turns of the coil, s=H/N is the turn-to-turn spacing (or helix pitch) of the coil, and _λ is the free space wavelength. Based on this relationship, the electrical length, or phase delay, of the helical coil is given by:

The principle is the same if the helix is helically wound or short and thick, but V _f and θ _c are easier to obtain experimentally. An expression for the characteristic (wave) impedance of a helical transmission line has also been derived as:

The spatial phase delay [theta] _y of the structure can be determined using the phase delay of the traveling wave of the vertical feeder conductor 221 (FIG. 7). The capacitance of a cylindrical vertical conductor above a perfect ground plane can be expressed as:

where _hw is the vertical length (or height) of the conductor and a is the radius in mk. For a helical coil, the phase delay of the traveling wave in the vertical feeder conductor can be given by:

where _βw is the propagation phase constant of the vertical feeder conductor, _hw is the vertical length (or height) of the vertical feeder conductor, Vw is the _velocity factor on the line, λ0 is the wavelength _at the supply frequency, and _λw is the slave velocity The propagation wavelength due to the factor _Vw . For a uniform cylindrical conductor, the rate factor is constant with Vw _≈0.94 , or in the range from about 0.93 to about 0.98. If the mast is considered to be a uniform transmission line, its average characteristic impedance can be approximated by the following formula:

where for a uniform cylindrical conductor Vw _≈ 0.94 for a uniform cylindrical conductor, and a is the radius of the conductor. An alternative representation that has been used in the amateur radio literature for the characteristic impedance of a single-wire feeder can be given by:

Equation (51) implies that _Zw for a single wire feed varies with frequency. The phase delay can be determined based on capacitance and characteristic impedance.

With the charging terminal T ₁ located above the lossy conducting medium 203 as shown in FIG. _eff ), or Φ=Ψ, to energize the charging terminal T ₁ . When this condition is met, the electric field generated by the charge Q ₁ oscillating on the charging terminal T ₁ is coupled into the guided surface waveguide mode traveling along the surface of the lossy conducting medium 203 . For example, if Brewster's angle (θ _i,B ), the phase delay (θ _y ) associated with vertical feeder conductor 221 (Fig. 7), and the configuration of coil 215 (Fig. 7) are known, then tap 224 (Fig. 7 ) can be determined and adjusted to apply an oscillating charge Q ₁ on the charging terminal T ₁ with phase Φ=Ψ. The position of the tap 224 can be adjusted to maximize the coupling of the traveling surface wave into the guided surface waveguide mode. Excessive coil length beyond the location of tap 224 may be removed to reduce capacitive effects. The vertical line height and/or geometric parameters of the helical coils can also be varied.

Coupling to the guided surface waveguide mode on the surface _of the lossy conducting medium 203 can be improved and/or optimized by tuning the guided surface waveguide probe 200 to the standing wave resonance for the complex mirror plane associated with the charge Q _on the charging terminal T . By doing so, the performance of the guided surface waveguide probe 200 can be tuned for increased and/or maximum voltage (and thus charge Q ₁ ) on the charging terminal T ₁ . Referring back to FIG. 3 , the effect of the lossy conducting medium 203 in zone 1 can be examined using the mirror image principle.

Physically, the raised charge Q1 lying above the perfectly conducting plane attracts the free charges _on the perfectly conducting plane, which then "accumulate" in the region below the raised charge _Q1 . The resulting distribution of "bound" charges on a perfectly conducting plane resembles a bell curve. The superposition _of the potential of the rising charge Q1 plus the potential of the induced "accumulated" charge below it promotes the zero equipotential surface of a perfectly conducting plane. The solution to the boundary value problem describing the field in the region above the perfectly conducting plane can be obtained using the classical concept of image charges, where the field from a raised charge is superimposed with the field from the corresponding "image" charge below the perfectly conducting plane .

This analysis can also be used for the lossy conducting medium 203 by assuming the existence of an effective image charge Q ₁ ′ beneath the guiding surface waveguide probe 200 . The effective image charge Q ₁ ′ coincides with the charge Q ₁ on the charge terminal T ₁ with respect to the conductive image ground plane 130 , as shown in FIG. 3 . However, the image charge Q1 _' is not only at some actual depth, but also ₁₈₀ ° opposite to the main source charge Q1 _on the charging terminal T1, as they would be in the case of a perfect conductor. Instead, lossy conducting medium 203 (eg, terrestrial medium) represents a phase-shifted mirror image. That is, the complex depth of the image charge Q ₁ ′ below the surface (or physical boundary) of the lossy conducting medium 203 . For a discussion of complex image depths, see Wait, JR, "Complex Image Theory—Revisited," IEEE Antennas and Propagation Magazine , Vol. 33, No. 4, August 1991, pp. 27-29, which is fully incorporated by reference included here.

Instead of an image charge Q ₁ ' at a depth equal to the physical height (H ₁ ) of the charge Q ₁ , a conductive image ground plane 130 (representing a perfect conductor) is at a complex depth z=-d/2, and the image charge Q ₁ ' is at The complex depth given by -D ₁ =-(d/2+d/2+H ₁ )≠H ₁ (ie "depth" has both magnitude and phase) occurs. For a vertically polarized source on the ground,

in

as indicated in equation (12). The complex spacing of the image charges in turn implies that the external field will experience an additional phase shift not encountered when the interface is a dielectric or a perfect conductor. In a lossy conducting medium, the wavefront normal is parallel to the tangent to the conductive mirrored ground plane 130 at z=-d/2 and not at the boundary interface between regions 1 and 2 .

Consider the case where the lossy conductive medium 203 illustrated in FIG. 8A is a finite conductive ground 133 with a physical boundary 136 . The finite conductive ground 133 can be replaced by a perfectly conductive mirrored ground plane 139 as shown in FIG. 8B , which lies at a complex depth z ₁ below the physical boundary 136 . This equivalent representation exhibits the same impedance when looking down into the interface at physical boundary 136 . The equivalent representation of Figure 8B can be modeled as an equivalent transmission line, as shown in Figure 8C. The cross-section of the equivalent structure is represented as a (z-direction) end-loaded transmission line, the impedance of this perfectly conductive mirror plane is short-circuited (z _s =0). The depth z ₁ can be determined by equating the TEM wave impedance looking down at earth with the mirrored ground plane impedance z _in looking into the transmission line of FIG. 8C .

In the case of FIG. 8A, the propagation constant and wave intrinsic impedance in the upper region (air) 142 are:

In a lossy ground 133, the propagation constant and wave intrinsic impedance are:

For normal incidence, the equivalent representation of FIG. 8B is equivalent to a TEM transmission line whose characteristic impedance is that of air (z _o ), has a propagation constant γ _o , and whose length is z ₁ . Thus, the mirrored ground plane impedance Z seen at the interface of the short transmission line of Figure _8C is given by:

Z _in =Z _o tanh(γ _o z ₁ ). (59)

Letting the mirrored ground plane impedance Z _in associated with the equivalent mode of Figure 8C be the same as the normal incident wave impedance _of Figure 8A and solving for z gives the distance to the short (perfectly conductive mirrored ground plane 139) as:

where only the first term of the serial extension of the inverse hyperbolic tangent is considered for this approximation. Note that in the air region 142, the propagation constant is γ _o = jβ _o , so Z _in = jZ _o tan β _o z ₁ (which is a completely imaginary quantity for the real number z ₁ ), but z _e is complex-valued if σ≠0 . Therefore, Z _in =Z _e only when z ₁ is a complex distance.

Because the equivalent representation of FIG. 8B includes a perfectly conductive mirrored ground plane 139, the mirror depth of a charge or current located at the earth's surface (physical boundary 136) is equal to the distance z ₁ on the other side of the mirrored ground plane 139, or at d=2×z ₁ below the Earth's surface (which is located at z=0). Therefore, the distance to a perfectly conductive mirrored ground plane 139 can be approximated by:

In addition, the "mirror charge" will be "equal and opposite" to the real charge, so the potential of a perfectly conductive mirror ground plane 139 at depth z ₁ =-d/2 will be zero.

If _a charge Q ₁ is raised at _a distance H ₁ above the earth's surface as shown in _FIG . The complex distance of d/2+H ₁ . The guided surface waveguide probe 200b of FIG. 7 can be modeled as an equivalent single-wire transmission line mirror plane model that can be based on the perfect conductive mirror ground plane 139 of FIG. 8B. Figure 9A shows an example of an equivalent single-wire transmission line mirror plane model, and Figure 9B illustrates an example of an equivalent classical transmission line model including the short-circuited transmission line of Figure 8C.

In the equivalent mirror plane model of Fig. 9A and Fig. 9B, Φ = θ _y + θ _c is the phase delay of the traveling wave of the guiding surface waveguide probe 200 referenced to the ground 133 (or lossy conducting medium 203), θ _c = β _p H is the electrical length of the coil 215 ( FIG. 7 ) of physical length H in degrees, θ _y = β _w h _w is the electrical length of the vertical feeder conductor 221 ( FIG. 7 ) of physical length h _w in degrees, and θ _d = β _o d/2 is the phase shift between the mirrored ground plane 139 and the physical boundary 136 of the earth 133 (or lossy conducting medium 203 ). In the example of FIGS. 9A and 9B , Z is the characteristic impedance of the raised vertical feeder conductor ₂₂₁ in ohms, Z is the characteristic impedance of the coil ₂₁₅ in ohms, and _Z is the characteristic of free space impedance.

At the base of the guided surface waveguide probe 200, the impedance "looking up" into the structure is Z _↑ = Z _base . where the load impedance is:

where _CT is the self _- capacitance of charging terminal T1, the impedance "looking up" into the vertical feedline conductor 221 (FIG. 7) is given by:

And the impedance "looking up" into coil 215 (FIG. 7) is given by:

At the base of the guided surface waveguide probe 200, the impedance "looking down" into the lossy conducting medium 203 is Z _↓ = Z _in , which is given by:

where Z _s =0.

Neglecting losses, the equivalent mirror plane model can be tuned to resonate at the physical boundary 136 when Z _↓ + Z _↑ = 0. Alternatively, in the low loss case, X _↓ + X _↑ = 0 at physical boundary 136 , where X is the corresponding reactive component. Thus, the impedance "looking up" to the physical boundary 136 in the guided surface waveguide probe 200 is the conjugate of the impedance "looking down" to the physical boundary 136 in the lossy conducting medium 203 . By adjusting the load impedance Z _L of the charging terminal T ₁ while maintaining the traveling wave phase delay Φ equal to the angle of the wave tilt Ψ of the medium such that Φ = Ψ, this improves and/or maximizes The coupling of the electric field of the probe to the guided surface waveguide mode of the surface of the ground), the equivalent mirror plane model of FIGS. 9A and 9B can be tuned to resonate relative to the mirrored ground plane 139. In this way, the impedance of the equivalent complex mirror plane model is purely resistive, which maintains a superimposed standing wave on the probe structure that maximizes the voltage and rising charge on terminal T1, and is expressed by equation ( ₁ )-( 3) and (16) maximize the propagating surface waves.

From the Hankel solution, the guided surface wave excited by the guided surface waveguide probe 200 is an outwardly propagating traveling wave . The source distribution along the feed network 209 ( FIGS. 3 and 7 ) between the charging terminal T ₁ and the ground pile 218 guiding the surface waveguide probe 200 actually consists of a superposition of traveling waves plus standing waves on the structure. With the charging terminal T ₁ located at or above the physical height h _p , the phase delay of the traveling wave moving through the feed network 209 matches the angle of wave inclination associated with the lossy conducting medium 203 . This mode matching allows the initiation of traveling waves along the lossy conducting medium 203 . Once the phase delay has been established for the traveling wave, the load impedance _{ZL of} the charging terminal T1 is adjusted so that the probe structure is directed to the mirrored ground plane (130 of FIG. 3 or 139 of FIG. 8 ) at complex depth -d/2 for the standing wave resonance. In this case, the impedance seen from the mirrored ground plane has zero reactance and the charge _on the charging terminal T1 is maximized.

The difference between traveling wave phenomena and standing wave phenomena is that (1) the phase delay (θ = βd) of a traveling wave over a portion of a transmission line (sometimes called a "delay line") of length d is due to a propagation time delay; however (2) The position-dependent phase of the standing wave (consisting of forward and backward propagating waves) depends on both the line length propagation time delay and the impedance transformation at the interface between line sections of different characteristic impedance. In addition to the phase delay due to the physical length of the transmission line section operating in sinusoidal steady state, there is an additional reflection coefficient phase at the impedance discontinuity due to the ratio _Zoa / _Zob , where _Zoa and _Zob are the two sections of the transmission line For example, the characteristic impedance of the helical coil portion Z _oa =Z _c ( FIG. 9B ) and the characteristic impedance of the straight line portion of the vertical feeder conductor Z _ob =Z _w ( FIG. 9B ).

As a result of this phenomenon, two relatively short transmission line sections of generally different characteristic impedances can be used to provide very large phase shifts. For example, a probe structure consisting of two sections of a transmission line, one low impedance and one high impedance, together with a total physical length of 0.05λ can be fabricated to provide a 90° phase shift equivalent to a 0.25λ resonance. This is due to the large jump in the characteristic impedance. In this way, the physically short probe structure can be electrically longer than the two physical lengths combined. This is illustrated in Figures 9A and 9B, where a discontinuity in impedance ratio provides a large jump in phase. The impedance discontinuity provides a substantial phase shift where the parts join together.

Referring to FIG. 10 , there is shown a flowchart 150 illustrating an example of adjusting a guided surface waveguide probe 200 ( FIGS. 3 and 7 ) to substantially mode match to a guided surface waveguide mode on the surface of a lossy conducting medium, the guided surface waveguide The modes initiate guided surface traveling waves along the surface of the lossy conducting medium 203 (FIG. 3). Starting at 153 , the charging terminal T ₁ of the guiding surface waveguide probe 200 is located at a defined height above the lossy conducting medium 203 . Using the properties of the _lossy conducting medium 203 and the operating frequency of the guided surface waveguide probe 200, one can find Hankel intersection distance. The complex refractive index (n) can be determined using Equation (41), and then the complex Brewster's angle (θ _i,B ) can be determined from Equation (42). The physical height ( _hp ) of charging terminal T ₁ can then be determined from equation (44). The charge terminal T ₁ should be at or above the physical height ( _hp ) in order to excite the distant component of the Hankel function. This height relationship is initially considered when surface waves are activated. In order to reduce or minimize the bound charge _on the charging terminal T1, the height should be at least four times the spherical diameter (or equivalent spherical diameter) _of the charging terminal T1.

At 156, the electrical phase delay Φ _of the rising charge Q1 _on the charging terminal T1 is matched to the complex wave tilt angle Ψ. The phase delay of the helical coil (θ _c ) and/or the phase delay of the vertical feedline conductor (θ _y ) can be adjusted such that Φ is equal to the angle (Ψ) of the wave tilt (W). Based on equation (31), the angle (Ψ) of wave inclination can be determined as follows:

The electrical phase Φ can then be matched to the angle of wave tilt. This angular (or phase) relationship is next considered when surface waves are activated. For example, the electrical phase delay Φ=θ _c +θ _y can be adjusted by changing the geometric parameters of the coil 215 ( FIG. 7 ) and/or the length (or height) of the vertical feeder conductor 221 ( FIG. 7 ). By matching Φ ₌ Ψ, an electric field can be established at or beyond the Hankel intersection distance ( _Rx ) with complex Brewster angles at the boundary interface to excite surface waveguide modes and along The lossy conducting medium 203 initiates a traveling wave.

Next at 159 , the load impedance of the charging terminal T ₁ is tuned to resonate the equivalent mirror plane model of the guided surface waveguide probe 200 . The depth (d/2) of the conductive mirrored ground plane 139 of FIGS. 9A and 9B (or 130 of FIG. 3 ) can be measured using equations (52), (53) and (54) and the lossy conductive medium 203 (e.g. , the value of the earth) is determined. Using this depth, the phase shift (θ _d ) between the mirrored ground plane 139 and the physical boundary 136 of the lossy conducting medium 203 can be determined using θ _d =β _o d/2. The impedance "looking down" into the lossy conducting medium 203 (Z _in ) can then be determined using equation (65). This resonance relationship can be taken into account to maximize the launched surface waves.

Based on the adjusted parameters of the coil 215 and the length of the vertical feeder conductor 221, the velocity factor, phase delay and impedance of the coil 215 and the vertical feeder conductor 221 can be determined using equations (45) to (51). In addition, the self-capacitance (C _T ) of the charging terminal T ₁ can be determined, for example, using equation (24). The propagation factor (β _p ) of the coil 215 can be determined using equation (35), and the propagation phase constant (β _w ) of the vertical feedline conductor 221 can be determined using equation (49). Using the self-capacitance and determined values of the coil 215 and vertical feedline conductor 221, the impedance of the guided surface waveguide probe 200 as "looking up" into the coil 215 can be determined using equations (62), (63) and (64) ( Z _base ).

By adjusting the load impedance Z _L , the equivalent mirror plane model of the guided surface waveguide probe 200 can be tuned to resonance, so that the reactance component X _{base of Z base cancels} the reactance component X _in of Z _in , or X _base +X _in =0 ,Come. Thus, the impedance "looking up" to the physical boundary 136 in the guided surface waveguide probe 200 is the conjugate of the impedance "looking down" to the physical boundary 136 in the lossy conducting medium 203 . The load impedance ZL can be adjusted by changing the capacitance ( _{C T} ) _of the charging terminal T1 without changing the electrical phase delay Φ _{= θc} + _θy of the charging terminal T1. An iterative scheme may be employed to tune the load impedance Z _L for the resonance of the equivalent mirror plane model with respect to the conductive mirror ground plane 139 (or 130 ). In this way, the coupling of the electric field along the surface of the lossy conducting medium 203 (eg, the ground) to the guided surface waveguide modes can be improved and/or maximized.

This can be better understood by illustrating the situation with numerical examples. Consider a guided surface waveguide probe 200 with a top-loaded vertical root comprising a physical height h _p with charging terminal T ₁ excited through _a helical coil and a vertical feeder conductor at an operating frequency (f _o ) of 1.85 MHz. For a height (H ₁ ) of 16 feet and a lossy conducting medium 203 (e.g., earth) with a relative permittivity ε _r =15 and a conductivity σ ₁ =0.010 mhos/m, several calculations can be made for f _o =1.850 MHz Surface wave propagation parameters. In these cases, the Hankel intersection distance can be found to be Rx ₌ 54.5 feet with a physical height of _hp = 5.5 feet, which is well below the actual height _of charging terminal T1. Although a charge terminal height H1 ₌ 5.5 feet can be used, the taller probe structure reduces bond capacitance, which allows _a greater percentage of free charge on the charge terminal T1, providing greater field strength and excitation of traveling waves.

The wavelength length can be determined as:

where c is the speed of light. From equation (41), the complex refractive index is:

where x = σ ₁ /ωε _o , and ω = 2πf _o , and from equation (42), the complex Brewster angle is:

Using equation (66), the wave tilt value can be determined as:

Therefore, the helical coil can be tuned to match Φ = Ψ = 40.614°

The velocity factor for a vertical feedline conductor (approximately a uniform cylindrical conductor with a diameter of 0.27 inches) can be given as Vw _≈0.93 . Since h _p << λ _o , the propagation phase constant of the vertical feeder conductor can be approximated as:

From equation (49), the phase delay of the vertical feeder conductor is:

θ _y =β _w h _w ≈β _w h _p =11.640°. (72)

By adjusting the phase delay of the helical coil such that _θc = 28.974° = 40.614° - 11.640°, Φ will be equal to Ψ to match the guided surface waveguide mode. To illustrate the relationship between Φ and Ψ, Figure 11 shows a plot of both over the frequency range. Since both Φ and Ψ are frequency dependent, it can be seen that their respective curves intersect each other at about 1.85 MHz.

For a helical coil with a conductor diameter of 0.0881 inches, a coil diameter (D) of 30 inches, and a turn-to-turn spacing (s) of 4 inches, the velocity factor for the coil can be determined using equation (45) as:

and the propagation factor from equation (35) is:

With _θc = 28.974°, the axial length of the solenoid helix (H) can be determined using equation (46) such that:

This height determines where on the helical coil the vertical feeder conductors are connected, resulting in a coil with 8.818 turns (N=H/s).

By adjusting the phase delay of the traveling wave in the coil and the vertical feedline conductor to match the wave tilt angle (Φ = θ _c + θ _y = Ψ), the load impedance (Z _L ) of the charging terminal T ₁ can be adjusted for guiding the surface waveguide probe 200 The standing wave resonance of the equivalent mirror plane model. From the measured permittivity, conductivity and permeability of the earth, the radial propagation constant can be determined using equation (57):

And the complex depth of the conductive mirror ground plane can be approximated from equation (52) as:

where the corresponding phase shift between the conductive mirrored ground plane and the physical boundary of the earth is given by:

θ _d = β _o (d/2) = 4.015 - j 4.73°. (78)

Using equation (65), the impedance "looking down" into the lossy conducting medium 203 (i.e., earth) can be determined as:

Z _in =Z _o tanh(jθ _d )=R _in +jX _in =31.191+j 26.27 ohms. (79)

By matching the reactive component (X _in ) "looking down" into the lossy conducting medium 203 with the reactive component (X _base ) "looking up" into the guided surface waveguide probe 200, the coupling into the guided surface waveguide mode can be made maximize. This can be achieved by adjusting the capacitance _of the charging terminal T1 without changing the phase delay of the traveling wave of the coil and the vertical feeder conductor. For example, by adjusting the charge terminal capacitance (C _T ) to 61.8126pF, the load impedance from equation (62) is:

and match the reactive component at the boundary.

Using equation (51), the impedance of the vertical feeder conductor (with a diameter (2a) of 0.27 inches) is given as:

and the impedance "looking up" into the vertical feeder conductor is given by equation (63):

Using equation (47), the characteristic impedance of the helical coil is given as:

and the impedance "looking up" into the coil at the base is given by equation (64) as:

When compared with the solution of equation (79), it can be seen that the reactive components are opposite and approximately equal, and are thus conjugates of each other. Thus, the impedance (Z _ip ) looking "up" from the perfectly conductive mirrored ground plane into the equivalent mirrored plane model of Figures 9A and 9B is simply resistance, or _Zip = R+j0.

When the electric field generated by the guided surface waveguide probe 200 (Fig. 3) is established by matching the phase delay of the traveling wave and the wave tilt angle of the feed network, and the probe structure is relative to a perfectly conductive mirror ground plane at complex depth z=-d/2 At resonance, the field is essentially mode matched to a guided surface waveguide mode on the surface of the lossy conducting medium, launching a guided surface traveling wave along the surface of the lossy conducting medium. As shown in Figure 1, the guided field strength curve 103 of the guided electromagnetic field has The characteristic decays exponentially and exhibits a distinguishing inflection point 109 on a log-log scale.

In summary, analytically and experimentally, the structural traveling wave component of the guided surface waveguide probe 200 has a phase delay (Φ) at its upper end matching the angle (Ψ) of the wave tilt of the surface traveling wave (Φ=Ψ). In this case, the surface waveguide can be said to be "mode matched". Additionally, the structurally resonant standing wave component of the guided surface waveguide probe 200 has V _MAX at the charging terminal T ₁ and V _MIN at the mirror plane 139 ( FIG. 8B ), where at complex depth z=-d/2 and Not at the junction at the physical boundary 136 of the lossy conducting medium 203, _Zip = _Rip + j0. (FIG. 8B). Finally, charging terminal T ₁ is at sufficient height H ₁ (h≥R _{x tanψ i,B} ) of FIG. do so, where Item is dominant. Receive circuitry may be used with one or more guided surface waveguide probes to facilitate wireless transmission and/or power transfer systems.

Referring back to FIG. 3 , the operation of the guided surface waveguide probe 200 may be controlled to adjust for changes in operating conditions associated with the guided surface waveguide probe 200 . For example, adaptive probe control system 230 may be used to control feed network 209 and/or charging terminal T1 to control operation of guided surface waveguide probe 200 . Operating conditions may include, but are not limited to, changes in the properties of the lossy conducting medium 203 (eg, conductivity σ and relative permittivity ε _r ), changes in field strength, and/or changes in the load guiding the surface waveguide probe 200 . As can be seen from equations (31), (41) and (42), the refractive index (n), complex Brewster angle ( θ _i,B ) and wave tilt (|W|e ^jΨ ).

Instruments such as conductivity measurement probes, permittivity sensors, geometers, field meters, current monitors, and/or load receivers can be used to monitor changes in operating conditions and provide information about current operating conditions to the Adaptive Probe Control System 230. Probe control system 230 may then make one or more adjustments to guided surface waveguide probe 200 to maintain specific operating conditions for guided surface waveguide probe 200 . For example, when the humidity and temperature change, the electrical conductivity of the soil will also change. Conductivity measurement probes and/or permittivity sensors may be located at various locations around guided surface waveguide probe 200 . In general, it may be desirable to monitor conductivity and/or permittivity at or around the _Hankel intersection distance Rx of the operating frequency. Conductivity measurement probes and/or permittivity sensors may be located at multiple locations around guided surface waveguide probe 200 (eg, in each quadrant).

The conductivity measurement probe and/or permittivity sensor may be configured to estimate the conductivity and/or permittivity on a periodic basis and communicate this information to the probe control system 230 . This information may be communicated to probe control system 230 over a network such as, but not limited to, a LAN, WLAN, cellular network, or other suitable wired or wireless communication network. Based on the monitored conductivity and/or permittivity, probe control system 230 can estimate changes in refractive index (n), complex Brewster angle (θ _i,B ), and/or wave tilt (|W|e ^jΨ ), and The guided surface waveguide probe 200 is tuned to maintain the phase delay (Φ) of the feed network 209 equal to the wave tilt angle (Ψ) and/or to maintain the resonance of the equivalent mirror plane model of the guided surface waveguide probe 200 . This can be achieved, for example, by adjusting θ _y , θ _c and/or _CT . For example, the probe control system 230 may adjust the self _- capacitance of the charge terminal T1 and/or the phase delay ( _θy , _θc ) applied to the charge terminal T1 to maintain the electric start _- up efficiency of the guided surface wave at or near a maximum . For example, the self _- capacitance of charging terminal T1 can be changed by changing the size of the terminal. Charge distribution can also be improved by increasing the size _of charge terminal T1, which reduces the _{chance of} discharge from charge terminal T1. In other embodiments, charging terminal T ₁ may include a variable _inductance that may be adjusted to vary load impedance ZL. _The phase applied to charging terminal T1 may be adjusted by changing the tap position on coil 215 (FIG. 7), and/or by including a plurality of predefined taps along coil 215 and switching between different predefined tap positions, to maximize startup efficiency.

Field or field strength (FS) meters may also be distributed around the guided surface waveguide probe 200 to measure the field strength of the field associated with the guided surface wave. The field or FS meter may be configured to detect field strength and/or changes in field strength (eg, electric field strength) and communicate this information to probe control system 230 . This information may be communicated to probe control system 230 over a network such as, but not limited to, a LAN, WLAN, cellular network, or other suitable communication network. As the load and/or environmental conditions change or change during operation, the guided surface waveguide probes 200 can be adjusted to maintain a specific field strength at the FS meter location to ensure proper power transfer to the receiver, and the load they provide.

For example, the phase delay (Φ = θ _y + θ _c ) applied to the charge terminal T ₁ can be adjusted to match the wave tilt angle (Ψ). By adjusting one or two phase delays, the guided surface waveguide probe 200 can be tuned to ensure that the wave tilt corresponds to a complex Brewster angle. This can be accomplished by adjusting the tap position on coil 215 (FIG. ₇ ) to vary the phase delay of the supply to charge terminal T1. _The voltage level supplied to the charging terminal T1 can also be increased or decreased to adjust the electric field strength. This can be achieved by adjusting the output voltage of the excitation source 212 or by adjusting or reconfiguring the feed network 209 . For example, the position of tap 227 (FIG. ₇ ) of AC source 212 may be adjusted to increase the voltage seen by charging terminal T1. Maintaining field strength levels within a predefined range can improve receiver coupling, reduce ground current losses, and avoid interference with transmissions from other guided surface waveguide probes 200 .

The probe control system 230 may be implemented in hardware, firmware, software executed by hardware, or a combination thereof. For example, probe control system 230 may include processing circuitry including a processor and memory, both of which may be coupled to a local interface, such as a data bus with an accompanying control/address bus, as will be appreciated by those skilled in the art like that. A probe control application may be executed by the processor to adjust the operation of the guided surface waveguide probe 200 based on the monitored conditions. Probe control system 230 may also include one or more network interfaces for communicating with various monitoring devices. Communications may be over a network such as, but not limited to, a LAN, WLAN, cellular network, or other suitable communication network. Probe control system 230 may include, for example, a computer system such as a server, desktop computer, laptop computer, or other systems with similar capabilities.

Referring back to the example of FIG. 5A , the complex angle trigonometry is shown for the incident electric field (E) of the charging terminal T ₁ with a complex Brewster angle (θ _i,B ) at the Hankel intersection distance (R _x ). Ray Optics Explained. Recall that for lossy conducting media, the Brewster's angle is complex and is specified by equation (38). Electrically, the geometric parameter is related by the electrical effective height (h _eff ) of the charging terminal T ₁ by equation (39). Since both the physical height (h _p ) and the Hankel intersection distance (R _x ) are real quantities, the angle of the required guided surface wave tilt (W _Rx ) at the Hankel intersection distance is equal to the complex effective height Phase (Φ) of (h _eff ). For a charging terminal T1 located at physical height _hp and excited with _a charge of appropriate phase Φ, the resulting electric field _is at the Hankel intersection distance Rx and incident on the lossy conductive medium boundary interface at Brewster's angle. Under these conditions, guided surface waveguide modes can be excited with no or substantially negligible reflections.

However, equation (39) implies that the physical height of the guided surface waveguide probe 200 may be relatively small. While this will excite guided surface waveguide modes, this may result in excessively large bound charges with little free variation. To compensate, the charge terminal T1 can be raised to _an appropriate level to increase the amount of free charge. As an example rule of thumb, charging terminal T ₁ may be located at an elevation of about 4-5 times (or more) the effective diameter of charging terminal T ₁ . Figure 6 illustrates the effect _of raising charging terminal T1 above the physical height ( _hp ) shown in Figure 5A. The increased elevation causes the distance of waves incident obliquely on the lossy conducting medium to shift beyond the Hankel intersection 121 (FIG. 5A). In order to improve the coupling in guided surface waveguide modes, and thus provide greater startup efficiency of guided surface waves, the lower compensation terminal T ₂ can be used to adjust the total effective height (h _TE ) of the charging terminal T ₁ such that at Hank Waves at the intersection distance are inclined at Brewster's angle.

Referring to FIG. 12 , there is shown an example of a guided surface waveguide probe 200c comprising a raised charging terminal T ₁ and a lower compensation terminal T ₂ arranged along a vertical axis z perpendicular to the plane represented by the lossy conducting medium 203 . _In this respect, the charging terminal T1 is directly above the compensation terminal T2, although some other arrangement of _two or more charging and/or compensation terminals _TN might be used. According to an embodiment of the present disclosure, the guided surface waveguide probe 200c is disposed above the lossy conducting medium 203 . The lossy conducting medium 203 constitutes region 1 , while the second dielectric 206 constitutes region 2 , and the second medium 206 shares a boundary interface with the lossy conducting medium 203 .

The guided surface waveguide probe 200c includes a feed network 209 that couples an excitation source 212 to a charging terminal T ₁ and a compensation terminal T ₂ . According to various embodiments, charges _Q1 and _{Q2 can} be applied to respective charge and compensation terminals _T1 and T2 _{depending on} the voltage applied to terminals T1 and T2 at any given moment. _I1 is the conduction current feeding the charge Q1 _on the charging terminal T1 via the terminal lead, and _I2 is the conduction current _feeding the charge _{Q2 on} the compensation terminal T2 via the terminal lead.

According to the embodiment of Fig. 12, the charging terminal T1 is located at _a physical height H1 above the lossy conductive medium 203, and the compensation terminal T2 is located at _a physical height _H2 directly below T1 along the vertical axis z, where _H2 is _{smaller than H1} . The height h of the transport structure can be calculated as h=H ₁ −H ₂ . The charging terminal T ₁ has an isolated (or self) capacitance C ₁ , and the compensation terminal T ₂ has an isolated (or self) capacitance C ₂ . _A mutual capacitance _CM may exist between terminals T1 and T2 depending _on the distance therebetween. During operation, depending _on the voltages applied to charging terminal T1 and compensating terminal T2 at any given moment, charges _Q1 and _Q2 are applied to charging terminal _T1 and compensating terminal _T2 , _respectively .

Referring next to FIG. 13 , there is shown a radiation optics interpretation of the effect produced by the elevated charge on the charging terminal T ₁ and compensating terminal T ₂ of FIG. 12 . With charging terminal T1 raised to _a height at which the ray intersects the lossy conducting medium at Brewster's angle at a distance greater _than the Hankel intersection point 121 as illustrated by line 163, compensation terminal T2 can be used to compensate for the increased Adjust h _TE for altitude. _The effect of the compensation terminal T2 is to reduce the electrical effective height of the guided surface waveguide probe (or effectively lift the lossy dielectric interface) so that the wave at the Hankel intersection distance is tilted at the Brewster angle, as illustrated by line 166.

The total effective height can be written as the superposition of the upper effective height (h _UE ) associated with the charging terminal T ₁ and the lower effective height (h _LE ) associated with the compensation terminal T ₂ such that:

where Φ _U is the phase delay applied to the upper charging terminal T1, Φ _L is the phase delay applied to the lower compensation terminal T2, β ₌ 2π/λ _p is the propagation factor from equation (35), _{and h p is} the charging _The physical height of terminal T1 and _hd is the physical height of compensating terminal _T2 . If the additional lead lengths are considered, they can be accounted for by adding the charging terminal lead length z to the physical height h _{p of} the charging terminal T1 and the compensation terminal lead length y to the physical height h _d of the compensation terminal _T2 as follows Shown:

The lower effective height can be used to adjust the total effective height (h _TE ) to equal the complex effective height (h _eff ) of FIG. 5A .

Equation (85) or (86 ₎ can be used to determine the physical height of the lower plate of the compensation terminal T2 and the phase angle of the feed terminal to obtain the desired wave tilt at the Hankel intersection distance. For example, equation (86) can be rewritten as _a phase shift applied to charging terminal T1 as a function of compensation terminal height ( _hd ) to give:

_In order to determine the positioning of the compensation terminal T2, the relationship described above can be used. First, the total effective height (h _TE ) is the superposition of the complex effective height (h _UE ) of the upper charging terminal T ₁ and the complex effective height (h _LE ) of the lower compensation terminal T ₂ , as expressed in equation (86). Afterwards, the tangent of the incident angle can be expressed geometrically as:

It is equal to the definition of wave tilt, W. Finally, given the desired Hankel intersection distance R _x , h _TE can be adjusted such that the wave tilt of the incident ray matches the complex Brewster angle at the Hankel intersection point 121 . This can be achieved by adjusting h _p , Φ _U and/or h _d .

These concepts are better understood when discussed in the context of the example of guided surface waveguide probes. Referring to FIG. 14 , there is shown an upper charging terminal T ₁ (e.g., a ball at height h _T ) and a lower compensation terminal T ₂ positioned along a vertical axis z substantially orthogonal to the plane represented by the lossy conductive medium 203. A graphical representation of an example of a guided surface waveguide probe _200d (eg, a disk at height hd). During operation, charges _Q1 and _Q2 are applied to charging terminal _T1 and compensation terminal _T2 , respectively, _{depending on} the voltage applied to terminals T1 and T2 at any given moment.

An AC source 212 is used as _an excitation source for the charging terminal T1, which is coupled to the guided surface waveguide probe 200d through a feed network 209 comprising a coil 215, such as a helical coil. The AC source 212 may be connected across the lower ends of the coil 215 via taps 227, as shown in Figure 14, or may be inductively coupled to the coil 215 by way of the main coil. Coil 215 may be coupled at a first end to ground stake 218 and at a second end to charging terminal T ₁ . In some implementations, the connection to charging terminal T ₁ can be adjusted using tap 224 at the second end of coil 215 . Compensation terminal T ₂ is located above and substantially parallel to lossy conductive medium 203 (eg, ground or earth) and is enabled by a tap coupled to coil 215 . A current meter 236 located between the coil 215 and the ground pile 218 may be used to provide an indication of the magnitude of the current (I ₀ ) at the base of the guiding surface waveguide probe. Alternatively, a current clamp may be used around the conductor coupled to ground stake 218 to obtain an indication of the magnitude of the current (I ₀ ).

In the example of FIG. 14 , coil 215 is coupled at a first end to ground stake 218 and is coupled at a second end to charging terminal T ₁ via vertical feeder conductor 221 . In some implementations, the connection to charging terminal T ₁ can be adjusted using tap 224 at the second end of coil 215 , as shown in FIG. 14 . The coil 215 may be energized by the AC source 212 at the operating frequency through a tap 227 on the lower portion of the coil 215 . In other implementations, AC source 212 may be inductively coupled to coil 215 through a primary coil. Compensation terminal T ₂ is enabled by tap 233 coupled to coil 215 . A current meter 236 located between the coil 215 and the ground stake 218 may be used to provide an indication of the magnitude of the current at the base of the guided surface waveguide probe 200d. Alternatively, a current clamp may be used around the conductor coupled to ground stake 218 to obtain an indication of the magnitude of the current. Compensation terminal T2 is located above and substantially parallel to lossy conductive medium 203 (eg, ground ₎ .

In the example of FIG. 14 , the connection to the charge terminal T ₁ on the coil 215 is above the connection point of the tap 223 for the compensation terminal T ₂ . This adjustment allows an increased voltage (and thus a higher charge Q ₁ ) to be applied to the upper charging terminal T ₁ . _In other embodiments, the connection points _of the charging terminal T1 and the compensation terminal T2 may be reversed. The overall effective height (h _TE ) of the guided surface waveguide probe 220d can be adjusted to excite an electric field with a guided surface wave tilt at the _Hankel intersection distance Rx. The Hankel intersection distance can also be found by equating the magnitudes of equations (20b) and (21) for -jγρ and solving for R _x as shown in FIG. 4 . Refractive index (n), complex Brewster angles (θ _i,B and ψ _i,B ), wave tilt (|W|e ^jΨ ) and complex effective height (h _eff = h _p e ^jΦ ) can be compared to the above equal Formulas (41)-(44) are determined.

With the selected charging terminal T1 configuration, the spherical diameter (or effective spherical diameter ₎ can be determined. For example, if the charging terminal T1 is not configured as _a sphere, the terminal configuration can be modeled as a spherical capacitance with an effective sphere diameter. _The size of charging terminal T1 may be chosen to provide _a sufficiently large surface area for charge Q1 to be applied on the terminal. _In general, it is desirable to make the charging terminal T1 as large as possible. _The size of the charging terminal T1 should be large enough to avoid ionization of the surrounding air, which could lead to discharge or sparks around the charging terminal. In order to reduce the amount _of bound charge on charge terminal T1, the desired increase in free charge _on charge terminal T1 that is used to initiate guided surface waves should be the effective spherical diameter above the lossy conducting medium (e.g., the earth) At least 4-5 times. The compensation terminal T ₂ can be used to adjust the overall effective height (h _TE ) of the guided surface waveguide probe 200d to excite an electric field with a guided surface wave _tilt at Rx. _The compensation terminal T2 may be located below the charging terminal _T1 at hd _{= hT -} hp, where hT is the total physical height _of the charging terminal _T1 . For a fixed position of the compensation terminal T2 and _a phase delay _ΦU applied to the upper charging terminal T1, the phase delay _ΦL applied to the lower compensation terminal _T2 can be determined using the relationship of equation (86 ₎ such that:

In an alternative embodiment, the compensation terminal T ₂ may be located at a height h _d where Im{Φ _L }=0. This is shown graphically in Fig. 15A, which shows plots 172 and 175 of the imaginary and real parts of Φ _U , respectively. Compensation terminal T ₂ is located at height h _d where Im{Φ _U }=0, as graphically illustrated by plot 172 . At this fixed height, the coil phase Φ _U can be determined from Re{Φ _U }, as graphically illustrated by plot 175 .

For AC source 212 coupled to coil 215 (eg, at the 50Ω point to maximize coupling), the position of tap 233 may be adjusted for compensation of parallel resonance of terminal _T2 with at least a portion of the coil at the operating frequency. 15B shows a schematic diagram of the general electrical hookup of FIG. ₁₄ , where V is the voltage applied from the AC source 212 to the lower portion of the coil 215 via the tap 227, and _V is the voltage supplied to the upper charging terminal T ₁ , and _V3 is the voltage applied to the lower compensation terminal _T2 through tap 233. Resistors _Rp and _Rd represent the ground return resistances _of charging terminal T1 and compensation terminal _T2 , respectively. _The charging terminal T1 and the compensation terminal _T2 can be configured as a sphere, cylinder, torus, ring, cap, or any other combination of capacitive structures. _The size _of charge terminal T1 and compensation terminal T2 may be chosen to provide a sufficiently large surface area for charges Q1 and _Q2 to be applied _on the terminals. _In general, it is desirable to make the charging terminal T1 as large as possible. _The size of the charging terminal T1 should be large enough to avoid ionization of the surrounding air, which could lead to discharges or sparks around the charging terminal. The self-capacitances C _p and C _d of the charging terminal T ₁ and the compensation terminal T ₂ can be determined, for example, using equation (24), respectively.

As seen in FIG. 15B , a resonant circuit is formed by at least a portion of the inductance of coil 215 , the self-capacitance C _d of compensation terminal T ₂ , and the ground return resistance R _d associated with compensation terminal T ₂ . Parallel resonance may be established by adjusting the voltage V ₃ applied to compensation terminal T ₂ (eg, by adjusting the position of tap 233 on coil 215 ) or by adjusting the height and/or size of compensation terminal T ₂ to adjust C _d . The position of the coil tap 233 can be adjusted for parallel resonance, which will cause the ground current through the ground pile 218 and through the ammeter 236 to reach a point of maximum. After the parallel resonance of the compensation terminal T2 has been established, the position of the tap 227 of the AC source 212 can be adjusted to the 50Ω point _on the coil 215 .

Voltage V2 from coil ₂₁₅ can be applied to charging terminal T1, and the position _of tap 224 can be adjusted so that the phase (Φ) of the total effective height ( _hTE ) _is approximately equal to that at the Hankel intersection distance (Rx) The angle of the guided surface wave tilt (W _Rx ). The position of the coil tap 224 can be adjusted until this operating point is reached, which causes the ground current through the ammeter 236 to increase to a maximum. In this regard, the resulting field excited by the guided surface waveguide probe 200d is substantially mode matched to the guided surface waveguide mode on the surface of the lossy conducting medium 203 , resulting in the initiation of guided surface waves along the surface of the lossy conducting medium 203 . This can be confirmed by measuring the field strength along the radial direction extending from the guided surface waveguide probe 200 .

_The resonance of the circuit including the compensation terminal T2 can be changed by addition _of the charging terminal T1 and/or adjustment _of the voltage applied to the charging terminal T1 by the tap 224 . While tuning the compensation terminal circuit for resonance aids subsequent adjustment of the charging terminal connection, it is not necessary to establish the guided surface wave tilt (W _Rx ) at the Hankel crossing distance (R _x ). The system can be further tuned to improve coupling by iteratively adjusting the position of tap 227 of AC source 212 to be at the 50Ω point on coil 215 , and adjusting the position of tap 233 to maximize ground current through ammeter 236 . When the position of taps 227 and 233 is adjusted, or when other components are added to coil 215, the resonance of the circuit including compensation terminal _T2 may shift.

_In other implementations, voltage V2 from coil 215 can be applied to charging terminal T1, and the position _of tap 233 can be adjusted such that the phase (Φ) of the total effective height ( _hTE ) _is approximately equal to that at Rx The angle (Ψ) at which the guided surface wave is tilted. The position of the coil tap 224 can be adjusted until an operating point is reached, which results in a substantially maximum ground current through the ammeter 236 . The resulting field is substantially mode matched to the guided surface waveguide mode on the lossy conducting medium 203 and the guided surface wave is launched along the surface of the lossy conducting medium 203 . This can be confirmed by measuring the field strength along the radial direction extending from the guided surface waveguide probe 200 . The system can be further tuned to improve by iteratively adjusting the position of tap 227 of AC source 212 at the 50Ω point on coil 215, and adjusting the position of taps 224 and/or 223 to maximize the ground current through ammeter 236 coupling.

Referring back to FIG. 12 , the operation of the guided surface waveguide probe 200 may be controlled to adjust for changes in operating conditions associated with the guided surface waveguide probe 200 . For example, the probe control system 230 may be used to control the positioning of the feed network 209 and/or the charging terminal T ₁ and/or the compensation terminal T ₂ to control the operation of the guided surface waveguide probe 200 . Operating conditions may include, but are not limited to, changes in the properties of the lossy conducting medium 203 (eg, conductivity σ and relative permittivity ε _r ), changes in field strength, and/or changes in the load guiding the surface waveguide probe 20 . As can be seen from equations (41)-(44), the refractive index (n), complex Brewster angle (θi _,B and ψ _i,B ), wave tilt (|W|e ^jΨ ) and complex effective height (h _eff = h _p e ^jΦ ).

Instruments such as conductivity measurement probes, permittivity sensors, geometers, field meters, current monitors, and/or load receivers can be used to monitor changes in operating conditions and provide information about current operating conditions to the Probe control system 230 . Probe control system 230 may then make one or more adjustments to guided surface waveguide probe 200 to maintain specific operating conditions for guided surface waveguide probe 200 . For example, when the humidity and temperature change, the electrical conductivity of the soil will also change. Conductivity measurement probes and/or permittivity sensors may be located at various locations around guided surface waveguide probe 200 . In general, it _is desirable to monitor conductivity and/or permittivity at or around the Hankel intersection distance Rx for this frequency of operation. Conductivity measurement probes and/or permittivity sensors may be located at multiple locations around guided surface waveguide probe 200 (eg, in each quadrant).

Referring then to FIG. 16 , there is shown an example of a guided surface waveguide probe 200 e comprising charging terminals T ₁ and T ₂ arranged along a vertical axis z. The guided surface waveguide probe 200e is disposed above the lossy conducting medium 203 constituting the region 1 . In addition, the second medium 206 shares a boundary interface with the lossy conducting medium 203 and constitutes a region 2 . The charging terminals T ₁ and T ₂ are located above the lossy conducting medium 203 . The charging terminal T1 is located at _a height H1, and the charging terminal T2 is located directly below T1 along the vertical axis z at _a height _H2 , where _H2 is smaller _{than H1} . The height h of the transmission structure represented by the guided surface waveguide probe 200e is h=H ₁ −H ₂ . Guided surface waveguide probe _200e includes _a feed network 209 that couples an excitation source 212 to charging terminals T1 and T2.

Charging terminals T ₁ and/or T ₂ include a conductive mass that can hold charge, which can be sized to hold as much charge as possible. Charging terminal T ₁ has a self-capacitance C ₁ and charging terminal T ₂ has a self-capacitance C ₂ , which can be determined using, for example, equation (24). Due to the placement of charging terminal T1 _directly above charging terminal T2, _a mutual capacitance C _M is created between charging terminals T1 and _{T2 .} Note that charging terminals T1 and _T2 need not be identical, but each can be of _a separate size and shape, and can comprise different conductive substances. Ultimately, the field strength of the guided surface wave initiated by the guided surface waveguide probe 200e is proportional to the amount _of charge on the terminal T1. The charge Q ₁ is in turn proportional to the self-capacitance C ₁ associated with the charging terminal T ₁ , since Q ₁ =C ₁ V, where V is the voltage applied at the charging terminal T ₁ .

The guided surface waveguide probe 200 e generates guided surface waves along the surface of the lossy conducting medium 203 when properly tuned to operate at a predefined operating frequency. The excitation source 212 may generate electrical energy at a predefined frequency that is applied to the guided surface waveguide probe 20Oe to excite the structure. When the electromagnetic field generated by the guided surface waveguide probe 20Oe is substantially mode matched to the lossy conducting medium 203, the electromagnetic field substantially synthesizes a wavefront incident at complex Brewster angles, resulting in little or no reflections. Therefore, the surface waveguide probe 200e does not generate radiated waves, but initiates guided surface traveling waves along the surface of the lossy conducting medium 203 . Energy from the excitation source may be delivered as a Zenneck surface current to one or more receivers located within the effective transmission range of the guided surface waveguide probe 20Oe.

One can determine the asymptotes of the radial Zenneck surface current J _ρ (ρ) on the surface of the lossy conducting medium 203 as J ₁ (ρ) approaching and J ₂ (ρ) moving away, where:

Approaching (ρ<λ/8):

away from (ρ>>λ/8): where _I1 is the conduction current feeding charge Q1 on the _first charging terminal T1 and _I2 is the conduction current feeding charge _{Q2 on} the _second charging terminal T2. The charge Q ₁ on the upper charging terminal T ₁ is determined by Q ₁ =C ₁ V ₁ , where C ₁ is the isolation capacitance of the charging terminal T ₁ . Note that for the Given above J ₁ there is a third component which complies with the Leontovich boundary condition and is contributed by the radial current in the lossy conducting medium 203 pumped by the quasi-static field of raised oscillating charge on the first charging terminal Q ₁ . The quantity Z _ρ = jωμ _o /γ _e is the radial impedance of the lossy conducting medium, where γ _e = (jωμ ₁ σ ₁ −ω ² μ ₁ ε ₁ ) ^1/2 .

The asymptotes representing the approach and divergence of the radial currents given by equations (90) and (91) are complex quantities. According to various embodiments, the physical surface current J(p)) is synthesized to match the current asymptote as closely as possible in magnitude and phase. That is, approaching |J(ρ)| is the tangent to |J ₁ | and moving away from |J(ρ)| is the tangent to |J ₂ |. Furthermore, according to various embodiments, the phase of J(ρ) should shift from a phase with J ₁ approaching to a phase with J ₂ moving away.

In order to match the guided surface wave mode at the point of transmission to initiate the guided surface wave, the phase of the surface current |J ₂ | moving away should be different from the phase of the surface current |J ₁ | The corresponding propagation phase plus a constant of about 45 degrees or 225 degrees. This is because for There are two roots, one near π/4 and one near 5π/4. The properly adjusted resultant radial surface current is:

Note that this is consistent with equation (17). Through Maxwell's equations, this J(ρ) surface current automatically creates a field according to:

Therefore, the phase difference between the surface current |J ₂ | moving away and the surface current |J ₁ | approaching for the guided surface wave mode to be matched is due to the fact that consistent with equations (1)-(3), the equation ( 93) - Properties of the Hankel function in (95). It is important to realize that the fields represented by equations (1)-(6) and (17) and equations (92)-(95) have the property of transmission line modes bound to lossy interfaces, rather than Radiation field associated with ground wave propagation.

To obtain the proper voltage magnitude and phase for a given design of guided surface waveguide probe 200e at a given location, an iterative scheme may be used. In particular, _a given excitation and configuration of the guided surface waveguide probe 200e can be performed taking into account the feed currents _of the terminals T1 and T2, the _{charges on} the charging terminals T1 and T2 and their mirror images in the lossy conducting medium 203 analysis in order to determine the resulting radial surface current density. This process may be performed iteratively until an optimal configuration and excitation for a given guided surface waveguide probe 20Oe is determined based on the desired parameters. To help determine whether a given guided surface waveguide probe 200e is operating at an optimal level, one can base on the region 1 conductivity (σ ₁ ) and region 1 permittivity (ε ₁ ) at the location of the guided surface waveguide probe 200e values, using equations (1)-(12), to generate the guided field strength curve 103 (FIG. 1). Such a guided field strength curve 103 may provide a basis of operation such that the measured field strength may be compared with the magnitude indicated by the guided field strength curve 103 to determine whether optimal transmission has been achieved.

Various parameters associated with guided surface waveguide probe 200e may be adjusted in order to achieve optimal conditions. One parameter that may be changed to tune the guiding surface waveguide probe 200e is the height of one or both of the charging terminals T ₁ and/or T ₂ relative to the surface of the lossy conducting medium 203 . _In addition, the distance or _spacing between the charging terminals T1 and T2 can also be adjusted. In doing so, one can minimize or otherwise modify the mutual capacitance _CM or any bonded capacitance between charging terminals T ₁ and T ₂ and lossy conductive medium 203 , as can be appreciated. It is also possible to adjust the size _of the respective charging terminals T1 and/or _T2 . By _varying the size of the charging terminals T1 and/or T2, as can be appreciated, _one will vary the respective self capacitance _C1 and/or C2 and mutual capacitance C _M .

Furthermore, another parameter that may be adjusted is the feed network 209 associated with the guided surface waveguide probe 20Oe. This can be achieved by adjusting the size of the inductive and/or capacitive reactances that make up the feed network 209 . For example, where such an inductive reactance comprises a coil, the number of turns on such a coil may be adjusted. Ultimately, adjustments to the feed network 209 may be made to alter the electrical length of the feed network 209, thereby affecting the voltage magnitude and phase _on the charging terminals T1 and _T2 .

Note that iterations of transmissions performed by making various adjustments may be accomplished through the use of computer models or by adjustments to physical structures, as can be appreciated. By making the above adjustments, _one can create corresponding "approaching" surface currents J and "away" approximating the same current J(ρ) of the guided surface wave mode specified in equations (90) and (91) above. Surface current J ₂ . In doing so, the resulting electromagnetic field will substantially or approximately mode match to the guided surface wave modes on the surface of the lossy conducting medium 203 .

Although not shown in the example of FIG. 16 , the operation of guided surface waveguide probe 200 e may be controlled to adjust for changes in operating conditions associated with guided surface waveguide probe 200 . For example, the probe control system 230 shown in FIG. 12 may be used to control the positioning and/or size of the feed network ₂₉₀ and/or charging terminals T1 and/or T2 to control the operation _of the guided surface waveguide probe 200e. Operating conditions may include, but are not limited to, changes in properties of the lossy conducting medium 203 (eg, conductivity σ and relative permittivity ε _r ), changes in field strength, and/or changes in the loading of the guiding surface waveguide probe 200e.

Referring now to FIG. 17, there is shown an example of the guided surface waveguide probe 20Oe of FIG. 16, here indicated as guided surface waveguide probe 20Of. Guided surface waveguide probe 200f includes charging terminals T ₁ and T ₂ positioned along a vertical axis z substantially normal to the plane represented by lossy conducting medium 203 (eg, earth). The second medium 206 is above the lossy conducting medium 203 . The charging terminal T ₁ has a self-capacitance C ₁ , and the charging terminal T ₂ has a self-capacitance C ₂ . During operation, charges _Q1 and _Q2 are applied across charge terminals T1 and _T2 , respectively, depending _on the voltage applied to charge terminals _T1 and _T2 at any given moment. Depending on the distance therebetween, there may be a mutual capacitance C _M between charging terminals T ₁ and T ₂ . Additionally, depending on the height of the respective charging terminals T ₁ and T ₂ relative to the lossy conductive medium 203 , there may be a bonded capacitance between the respective charging terminals T ₁ and T ₂ and the lossy conductive medium 203 .

Guided surface waveguide probe 200f includes a feed network 209 that includes an inductive impedance including a coil L _1a having a pair of leads coupled to a respective one of charging terminals T ₁ and T ₂ . In one embodiment, the designated coil L _1a has an electrical length of half (1/2) the wavelength at the operating frequency of the guided surface waveguide probe 200f.

Although the electrical length of coil L _1a is specified to be approximately one-half (1/2) of the wavelength at the frequency of operation, it is understood that coil L _1a may be specified to have an electrical length at other values. According to one embodiment, the fact that the coil L _1a has an electrical length of approximately half the wavelength at the operating frequency provides the advantage of creating a maximum voltage differential across the charging terminals T ₁ and T ₂ . However, when adjusting the guided surface waveguide probe 200f to obtain optimal excitation of the guided surface wave mode, the length or diameter of the coil L _1a can be increased or decreased. Coil length adjustment can be provided by taps located at one or both ends of the coil. In other embodiments, this may be the case where the inductive impedance is specified to have an electrical length significantly less than or greater than 1/2 the wavelength at the operating frequency of the guided surface waveguide probe 200f.

The excitation source 212 may be magnetically coupled to the feed network 209 . In particular, excitation source 212 is coupled to coil L _P that is inductively coupled to coil L _P of coil _{L 1a} . This can be achieved by link coupling, tapped coils, variable reactance, or other coupling methods as will be appreciated. To this end, the coil L _P is used as the primary coil, and the coil L _1a is used as the secondary coil, as can be understood.

_In order to tune the guided surface waveguide probe 200f for the desired guided surface wave transmission, the height _of the respective charging terminals T1 and T2 can be altered relative to the lossy conducting medium 203 and relative to each other. _In addition, the size _of the charging terminals T1 and T2 can be changed. Additionally, the size of coil L _{1a may be altered by adding or removing turns, or by changing some other dimension of coil L 1a .} Coil L _1a may also include one or more taps for adjusting the electrical length as shown in FIG. 17 . It is also possible to adjust the position _of the tap connected to the charging terminal T1 or _T2 .

Referring next to Figures 18A, 18B, 18C and 19, examples of general receive circuits for using surface guided waves in a wireless power transfer system are shown. 18A and 18B-18C include a linear probe 303 and a tuned resonator 306, respectively. FIG. 19 is a magnetic coil 309 according to various embodiments of the present disclosure. According to various embodiments, each of linear probe 303, tuned resonator 306, and magnetic coil 309 may be employed to receive power transmitted in the form of guided surface waves on the surface of lossy conducting medium 203 according to various embodiments. . As noted above, in one embodiment, lossy conducting medium 203 comprises terrestrial medium (or the earth).

With particular reference to FIG. 18A , the open circuit terminal voltage at the output 312 of the linear probe 303 depends on the effective height of the linear probe 303 . For this purpose, the terminal point voltage can be calculated as:

where _{E inc} is the intensity of the incident electric field induced on the linear probe 303 in volts per meter, dl is the integral element along the direction of the linear probe 303 , and he is the effective height of the linear probe 303 . Electrical load 315 is coupled to output 312 through impedance matching network 318 .

When linear probe 303 is subjected to guided surface waves as described above, a voltage is generated across output 312 which may be applied to electrical load 315 through conjugate impedance matching network 318, as the case may be. To facilitate the flow of power to electrical load 315, electrical load 315 should be substantially impedance matched to linear probe 303, as will be described below.

Referring to FIG. 18B , a ground current excitation coil 306 a possessing a phase shift equal to the wave tilt of the guided surface wave includes a charge terminal _TR raised (or suspended) above the lossy conductive medium 203 . The charging terminal T _R has a self-capacitance _CR . In addition, depending on the height of the charging terminal _TR above the lossy conducting medium 203 , there may also be a bonding capacitance (not shown) between the charging terminal _TR and the lossy conducting medium 203 . Bond capacitance should preferably be minimized as much as possible, although this is not entirely necessary in every case.

The tuned resonator 306a also includes a receiver network comprising a coil _LR with a phase shift Φ. One end of the coil _{LR is coupled to the charging terminal T R ,} and the other end of the coil _LR is coupled to the lossy conductive medium 203 . The receiver network may comprise vertical supply line conductors coupling the coil _LR to the charging terminal _TR . To this end, the coil _LR (which may also be referred to as tuned resonator _LR - _CR ) comprises a serially tuned resonator, since the charging terminal _CR and the coil _LR are arranged in series. The phase delay of the coil _LR can be adjusted by changing the size and/or height of the charging terminal _TR , and/or adjusting the size of the coil _LR so that the phase of the structure Φ is substantially equal to the angle Ψ of the wave tilt . It is also possible to adjust the phase delay of the vertical supply lines, eg by changing the length of the conductors.

For example, the reactance represented by the self-capacitance C _R is calculated as 1/jωC _R . Note that the total capacitance of the structure 306a may also include the capacitance between the charging terminal _TR and the lossy conductive medium 203, wherein the total capacitance of the structure 306a may be calculated from both the self capacitance _CR and any bonded capacitance, as can be understand that. According to one embodiment, the charging terminal _TR may be raised to a height such that any tie capacitance is substantially reduced or eliminated. The presence of bonded capacitance may be determined from capacitance measurements between the charging terminal _TR and the lossy conductive medium 203, as previously discussed.

The inductive reactance represented by the discrete element coil _LR can be calculated as jωL, where L is the lumped element inductance of the coil _LR . If the coil _LR is a distributed element, its equivalent end-point inductive reactance can be determined by traditional schemes. To tune the structure 306a, one can make adjustments such that the phase delay is equal to the wave tilt for the purpose of mode matching to the surface waveguide at the frequency of operation. In this case, the receiving structure can be said to be "mode matched" to the surface waveguide. A transformer link and/or impedance matching network 324 around the structure may be inserted between the probe and electrical load 327 to couple power to the load. Inserting an impedance matching network 324 between the probe terminals 321 and the electrical load 327 can affect the conjugate matching condition for maximum power transfer to the electrical load 327 .

Power will be delivered from the surface guided wave to the electrical load 327 when placed in the presence of surface currents at the operating frequency. To this end, the electrical load 327 may be coupled to the structure 306a by means of magnetic coupling, capacitive coupling or conductive (direct tap) coupling. The elements of the coupling network may be centralized components or distributed elements, as will be appreciated.

In the embodiment shown in Fig. 18B, a magnetic coupling is employed wherein the coil _LS is located on the secondary side with respect to the coil _LR used as the primary of the transformer. As can be appreciated, the coil _LS can be link coupled to the coil _LR by geometrically winding it around the same core structure and adjusting the coupled magnetic flux. Additionally, while the receiving structure 306a includes serially tuned resonators, appropriately phase delayed parallel tuned resonators or even distributed element resonators may also be used.

Although a receiving structure immersed in an electromagnetic field can couple energy from the field, it is understood that polarization-matched structures work best by maximizing coupling, and should obey existing rules for probe coupling to waveguide modes. For example, a TE ₂₀ (transverse electrical mode) waveguide probe may be optimal for extracting energy from a conventional waveguide excited in the TE ₂₀ mode. Similarly, in these cases, mode-matched and phase-matched receive structures can be optimized for coupling power from surface-guided waves. The guided surface wave excited by the guided surface waveguide probe 200 on the surface of the lossy conducting medium 203 can be considered as a waveguide mode of an open waveguide. Excluding waveguide losses, the source energy can be fully recovered. Useful receiving structures may be coupled E-fields, coupled H-fields, or excited surface currents.

The receiving structure may be tuned to increase or maximize coupling to the guided surface waves based on the local properties of the lossy conducting medium 203 in the vicinity of the receiving structure. To achieve this, the phase delay (Φ) of the receiving structure can be adjusted to match the angle (Ψ) of the wave tilt of the surface traveling wave at the receiving structure. If properly configured, the receiving structure can be tuned for resonance with respect to a perfectly conductive mirror ground plane at complex depth z=-d/2.

For example, consider a receive structure comprising the tuned resonator 306a of Figure 18B, comprising a coil _LR and a vertical supply line connected between the coil _LR and the charging terminal _TR . For a charging terminal T _R located at a defined height above the lossy conducting medium 203, the total phase shift Φ of the coil _LR and the vertical supply line can be matched to the angle (Ψ) of the wave tilt at the tuned resonator 306a. From equation (22), it can be seen that the wave passes obliquely and asymptotically:

where _εr includes the relative permittivity, and σ1 is the conductivity _of the lossy conducting medium 203 at the location of the receiving structure, εo is the permittivity of free space, and ω=2πf, where _f is the frequency of the excitation. Therefore, the wave tilt angle (Ψ) can be determined from equation (97).

The total phase shift (Φ = θ _c + θ _y ) of the tuned resonator 306a includes both the phase delay (θ _c ) through the coil LR and the phase delay (θ _y ) of the vertical supply line. The spatial phase delay along the conductor length _lw of the vertical supply line can be given by _θy = _{βw lw} , where _βw is the propagation phase constant of the vertical supply line conductor. Since the phase delay of the coil (or helical delay line) is θ _c = β _p l _C , where l _C is a physical constant and the propagation factor is:

where Vf is the _velocity factor on the structure, λ0 is the wavelength _at the supply frequency, and _λp is the propagation wavelength resulting from the _velocity factor Vf. One or two phase delays (θ _c +θ _y ) can be adjusted to match the phase shift Φ to the angle (Ψ) of wave tilt. For example, the tap position can be adjusted on the coil _LR of FIG. 18B to adjust the coil phase delay (θ _c ) to match the total phase shift to the wave tilt angle (Φ=Ψ). For example, the coil locations can be bypassed by tap connections, as shown in Figure 18B. The vertical supply line conductor can also be connected to the coil _LR via a tap, its position on the coil can be adjusted to match the total phase shift to the wave tilt angle.

Once the phase delay (Φ) of the tuned resonator 306a has been adjusted, the impedance of the charging terminal _TR can be adjusted to tune to resonate with respect to a perfectly conductive mirror ground plane at complex depth z=-d/2. This can be achieved by adjusting the capacitance _of the charging terminal T without changing the phase delay of the traveling wave of the coil _LR and the vertical supply line. This adjustment is similar to the adjustment described with respect to Figures 9A and 9B.

The impedance "looking down" into the lossy conducting medium 203 to the complex mirror plane is given by:

Z _in = R _in + jX _in = Z _o tanh(jβ _o (d/2)), (99)

in For vertically polarized sources above the earth, the depth of the complex mirror plane can be given by:

Where μ ₁ is the dielectric constant of the lossy conducting medium 203, and ε ₁ =ε _r ε _o .

At the base of the tuned resonator 306a, the impedance "looking up" into the receiving structure is Z _↑ = Z _base , as shown in FIG. 9A . where the terminal impedance is:

where _CR is the self-capacitance of the charge terminal _TR , the impedance in the vertical supply line conductor "looking up" into the tuned resonator 306a is given by:

And the impedance in the coil _LR "looking up" into the tuned resonator 306a is given by:

By matching the reactive component (X _in ) "looking down" into the lossy conducting medium 203 with the reactive component (X _base ) "looking up" into the tuned resonator 306a, it is possible to maximize the coupling.

Referring next to Figure 18C, an example of a tuned resonator 306b that does not include a charge terminal _TR on top of the receiving structure is shown. In this embodiment, tuned resonator 306b does not include a vertical supply line coupled between coil _LR and charge terminal _TR . Therefore, the total phase shift (Φ) of the tuned resonator 306b includes only the phase delay (θ _c ) through the coil _LR . As for the tuned resonator 306a of FIG. 18B, the coil phase delay _θc can be adjusted to match the angle of wave tilt (Ψ) determined from equation (97), which results in Φ=Ψ. While power extraction is possible for the receiving structure coupled into surface waveguide modes, it is difficult to tune the receiving structure to maximize the coupling to guided surface waves without the variable reactive load provided by the charging terminal _TR .

Referring to FIG. 18D , a flowchart 180 illustrating an example of tuning a receiving structure to substantially mode match a guided surface waveguide mode on the surface of a lossy conducting medium 203 is shown. Beginning at 181, if the receiving structure includes a charging terminal _TR (eg, the charging terminal of the tuned resonator 306a of FIG _. The physical height (h _p ) of the charging terminal T _R may be lower than the effective height because the surface guided wave has already been established by the guided surface waveguide probe 200 . The physical height may be chosen to reduce or minimize bonded charge on the charging terminal _TR (eg, four times the spherical diameter of the charging terminal). If the receiving structure does not include a charge terminal _TR (eg, the charge terminal of the tuned resonator 306b of FIG. 18C ), flow proceeds to 187 .

At 187 , the electrical phase delay Φ of the receiving structure matches the complex wave tilt angle Ψ defined by the local properties of the lossy conducting medium 203 . The phase delay of the helical coil (θ _c ) and/or the phase delay of the vertical supply line (θ _y ) can be adjusted such that Φ is equal to the angle (Ψ) of the wave tilt (W). The angle (Ψ) of wave tilt can be determined from equation (86). The electrical phase Φ can then match the angle at which the waves are tilted. For example, the electrical phase delay Φ = θ _c + θ _y can be adjusted by changing the geometrical parameters of the coil _LR and/or the length (or height) of the vertical supply line conductor.

Next at 190, the load impedance of the charge terminal _TR may be tuned to resonate the equivalent mirror plane mode of the tuned resonator 306a. The depth (d/2) of the conductive mirrored ground plane 139 (FIG. 9A) below the receiving structure can be determined using equation (100) and values of the lossy conductive medium 203 (eg, earth) at the receiving structure that can be measured locally. Using complex depths, the phase shift (θ _d ) between the mirrored ground plane 139 and the physical boundary 136 ( FIG. 9A ) of the lossy conducting medium 203 can be determined using θ _d =β _o d/2. The impedance "looking down" into the lossy conducting medium 203 (Z _in ) can then be determined using equation (99). This resonance relationship can be taken into account to maximize the coupling to the guided surface waves.

Based on the adjusted parameters of coil _LR and the length of the vertical supply line conductor, the rate factor, phase delay, and impedance of coil _LR and vertical supply line can be determined. In addition, the self-capacitance (C _R ) of the charging terminal T _R can be determined, for example, using equation (24). The propagation factor (β _p ) of the coil _LR can be determined using equation (98), and the propagation phase constant (β _w ) of the vertical supply line can be determined using equation (49). Using the self-capacitance, and determined values of the coil _LR and the vertical supply line, the impedance of the tuned resonator 306a "looking up" into the coil _LR can be determined using equations (101), (102) and (103) (Z _base ).

The equivalent mirror plane model of FIG. 9A is applied to the tuned resonator 306a of FIG. 9B. The tuned resonator 306a can be tuned by adjusting the load impedance Z _R of the charging terminal T _R such that the reactive component X _{base of Z base cancels} the reactive component X _in of Z _in , or X _base +X _in =0. Thus, the impedance at the physical boundary 136 ( FIG. 9A ) “looking up” into the coil of tuned resonator 306a is the conjugate of the impedance at the physical boundary 136 “looking down” into the lossy conducting medium 203 . The load impedance Z _R can be adjusted by changing the capacitance ( _CR ) of the charging terminal T _R without changing the electrical phase delay Φ = θ _c + θ _y seen by the charging terminal T _R . An iterative scheme may be employed to tune the load impedance Z _R for the resonance of the equivalent mirror plane model with respect to the conductive mirror ground plane 139 . In this way, the coupling of the electric field along the surface of the lossy conducting medium 203 (eg, the ground) to the guided surface waveguide modes may be improved and/or maximized.

Referring to FIG. 19 , the magnetic coil 309 includes a receive circuit coupled to an electrical load 336 through an impedance matching network 333 . To facilitate the reception and/or extraction of electrical energy from the guided surface waves, the magnetic coil 309 may be positioned such that the magnetic flux of the guided surface waves By passing through the magnetic coil 309 , a current is thereby induced in the magnetic coil 309 and a terminal voltage is generated at its output 330 . The magnetic flux of a guided surface wave coupled to a single-turn coil is expressed by:

in is the coupled magnetic flux, μ _r is the effective relative permittivity of the iron core of the magnetic coil 309, μ _o is the permittivity of free space, is the incident magnetic field intensity vector, is a unit vector orthogonal to the cross-section of the turns, and A _CS is the area enclosed by each loop. For an N-turn magnetic coil 309 oriented for maximum coupling to an incident magnetic field uniform across the cross-section of the magnetic coil 309, the open-circuit induced voltage appearing at the output 330 of the magnetic coil 309 is:

where variables are defined as above. The magnetic coil 309 can be tuned to the guided surface wave frequency, connected across its output 330 as a distributed resonator or an external capacitor, as possible, and then impedance matched to an external electrical load 336 by a conjugate impedance matching network 333 .

Assuming that the resulting circuit represented by magnetic coil 309 and electrical load 336 is properly tuned and conjugate impedance matched via impedance matching network 333 , the current induced in magnetic coil 309 can be employed to optimally power electrical load 336 . The receiving circuit represented by the magnetic coil 309 offers the advantage that it does not have to be physically connected to ground.

Referring to Figures 18A, 18B, 18C, and 19, each of the receive circuits represented by linear probe 303, mode matching structure 306, and magnetic coil 309 facilitate receiving transmissions from any of the embodiments of guided surface waveguide probe 200 described above. of electric energy. To this end, the received energy may be used to supply power to electrical loads 315/327/336 via a conjugate matching network, as can be appreciated. This is in contrast to a signal sent in the form of a radiated electromagnetic field that can be received in a receiver. Such signals have very low power available, and receivers of such signals do not load the transmitter.

The current guided surface wave generated using the guided surface waveguide probe 200 described above is also characterized in that the receiving circuit, represented by the linear probe 303, the mode matching structure 306 and the magnetic coil 309, applies a load to the excitation source 212 of the guided surface waveguide probe 200 ( For example, Figs. 3, 12 and 16), thereby generating a guided surface wave experienced by such a receiving circuit. This reflects the fact that the guided surface waves generated by a given guided surface waveguide probe 200 described above include transmission line modes. By way of contrast, the power source driving the radiating antenna generating the radiated electromagnetic waves is not loaded by the receivers, regardless of the number of receivers employed.

Thus, together with one or more guided surface waveguide probes 200 and one or more receive circuits in the form of linear probes 303 , tuned mode-matching structures 306 and/or magnetic coils 309 , a wireless distribution system can be formed. Given that the transmission distance of a guided surface wave using a guided surface waveguide probe 200 as proposed above is frequency dependent, it is possible to achieve wireless power distribution over a wide area or even globally.

Traditional wireless power transfer/distribution systems that are now widely studied include "energy harvesting" from radiated fields and sensors coupled to inductive or reactive near-fields. In contrast, the wireless power system wastes no power in the form of radiation, which is lost forever if not intercepted. The wireless power systems of the present disclosure are also not limited to extremely short distances like conventional mutual reactance coupled near-field systems. The wireless power system probes disclosed herein are coupled to novel surface-guided transmission line modes that are equivalent to delivering power to a load through a waveguide, or to a load directly wired to a remote power generator. Disregarding the power required to maintain the transmitted field strength plus the power dissipated in the surface waveguide (which is insignificant at very low frequencies relative to the transmission losses of conventional high voltage power lines at 60 Hz), all generator power reaches only expected electrical load. When the electrical load needs to be terminated, the source power generation is relatively idle.

Reference is next made to Figures 20A-E, which illustrate examples of various schematic symbols used with reference to the discussion below. Referring specifically to Figure 20A, there is shown a symbol representing any one of the guided surface waveguide probes 200a, 200b, 200c, 200e, 200d or 200f or any variation thereof. In the figures and discussions that follow, the description of this symbol is referred to as a guided surface waveguide probe P. For simplicity in the discussion below, any reference to a guided surface waveguide probe P is a reference to any of the following: guided surface waveguide probes 200a, 200b, 200c, 200e, 200d or 200f or variations thereof.

Similarly, reference is made to FIG. 20B, which shows a symbol representing a guided surface wave receiving structure, which may include a linear probe 303 (FIG. 18A), a tuned resonator 306 (FIGS. 18B-18C), or a magnetic coil 309 (FIG. 19). any of . In the following figures and discussions, the description of this symbol will be referred to as a guided surface wave receiving structure R. For simplicity, in the following discussion, any reference to the guided surface wave receiving structure R is a reference to any one of the linear probe 303, tuned resonator 306, or magnetic coil 309; or variations thereof.

In addition, referring to FIG. 20C, there is shown a symbol specifically representing the linear probe 303 (FIG. 18A). In the following figures and discussions, the description of this symbol is referred to as the guided surface wave receiving structure _Rp . For simplicity in the following discussion, any reference to the guided surface wave receiving structure R _P is a reference to the linear probe 303 or variations thereof.

In addition, referring to FIG. 20D, there is shown notation specifically representing the tuned resonator 306 (FIGS. 18B-18C). In the following figures and discussions, the description of this symbol is referred to as the guided surface wave receiving structure R _R . For simplicity in the discussion below, any reference to the guided surface wave receiving structure _RR is a reference to the tuned resonator 306 or variations thereof.

In addition, referring to FIG. 20E, there is shown a symbol specifically representing the magnetic coil 309 (FIG. 19). In the following figures and discussions, the description of this symbol is referred to as the guided surface wave receiving structure R _M . For simplicity in the discussion below, any reference to the guided surface wave receiving structure R _M is a reference to the magnetic coil 309 or variations thereof.

Referring to Figures 21-27, various embodiments of using guided surface waves emitted from a guided surface wave waveguide probe P to locate a position are disclosed. The navigation device detects a plurality of guided surface waves emitted from a plurality of guided surface wave waveguide probes P. By analyzing the time difference regarding the arrival of the guided surface waves, the time it takes for each guided surface wave to travel from the corresponding guided surface wave waveguide probe P to the position of the navigation device, compared with the original intensity of the guided surface wave at the position of the navigation device The difference in the intensity of the guided surface waves of , the phase shift between the guided surface waves measured at the position of the navigator, or some combination of these methods, can determine the position of the navigator on the earth. Additionally, in some embodiments, the navigation device may be powered by one or more guided surface waves. Additionally, guided surface waves could be used for time synchronization to improve the accuracy of navigation aids and/or other devices.

The range of the guided surface wave depends on the frequency of the guided surface wave. For example, guided surface waves having a frequency of about 20 kHz or less can travel around the Earth. At these frequencies, various embodiments of the present disclosure can be used for global positioning and navigation. Higher frequencies will travel shorter distances, such as hundreds or tens of miles, limiting various embodiments to area use for location and navigation.

Referring specifically to FIG. 21 , a navigation unit 400 is shown in accordance with various embodiments. The navigation unit 400 includes a receiver 403 , an antenna mount 406 and a computing device 409 . Receiver 403 is connected to antenna mount 406 , which in turn is connected to computing device 409 . In some embodiments, the navigation unit 400 may include a display. In such embodiments, the display may include, for example, one or more devices such as a liquid crystal display (LCD) display, a gas plasma-based flat panel display, an organic light emitting diode (OLED) display, an electronic ink (E Ink) display, an LCD Projectors or other types of display devices, etc.

In some embodiments, all or part of the navigation unit 400 may be enclosed in an external housing that protects the various components of the navigation unit 400 . For example, in some embodiments, navigation unit 400 may be a portable or handheld unit in which receiver 403, antenna mount 406, and computing device 409 are housed within a single housing. Such embodiments may include mobile computing devices, such as tablet computers, cellular phones, smart phones, personal digital assistants (PDAs), and/or similar mobile computing devices. Such embodiments may also include a dedicated navigation unit, such as a personal navigation device, handheld navigation device or navigation device that may be mounted to the dashboard of a bus, car, jet ski or similar vehicle. In other embodiments, receiver 403 may be remote or external to computing device 409 and connected to the computing device via antenna bracket 406 . Such embodiments may include, for example, a vehicle navigation unit 400 such as those found on ships or on airplanes.

Receiver 403 may correspond to one or more structures capable of receiving guided surface waves. Receiver 403 may include, for example, a linear probe, a tuned resonator, a magnetic coil, and/or similar structures for receiving guided surface waves, as described above. In some embodiments, receiver 403 may represent a plurality of receivers 403 , where each receiver is tuned to receive guided surface waves at a different frequency than the other receivers 403 . In various embodiments, receiver 403 may be configured to be tuned to simultaneously receive multiple guided surface waves at different frequencies. In some embodiments, receiver 403 may be configured to alternate frequencies to detect, receive and/or measure guided surface waves at a first frequency, then switch to a second frequency to detect a second guided surface wave at a second frequency Wave. Antenna bracket 406 may correspond to any physical structure capable of connecting receiver 403 to computing device 409 .

Computing device 409 includes at least one processor circuit, eg, with a processor 413 and memory 416 , both coupled to a local interface 419 . Local interface 419 may include, for example, a data bus with an accompanying address/control bus or other bus structure, as will be appreciated.

Stored in memory 416 are data and several components executable by processor 413 . Specifically, stored in the memory 416 and executable by the processor 413 is a multilateration application 423 and potentially other applications. Also stored in memory 416 may be data store 426, which may store map data 429, inertial data 431, phase shift curves 433, and/or potentially other data. Additionally, an operating system may be stored in the memory 416 and executable by the processor 413 .

Map data 429 represents one or more geographic locations where navigation unit 400 may be navigating or where geolocation may occur. Map data 429 may include global data or data related to a particular area or territory such as a hemisphere, continent, ocean, sea, lake, country, state/province, city, and/or portion thereof. Map data 429 may also include one or more coordinate systems for identifying locations on a sphere or within a particular area or venue. Such coordinate systems may include lines of latitude and longitude, a Universal Transverse Mercator (UTM) coordinate system, a Universal Polar Spherical Projection (UPS) coordinate system, a grid system, and/or other coordinate systems.

Inertial data 431 represents navigation data describing the current and historical trajectory of navigation unit 400 . Inertial data 431 may represent, for example, the current velocity, current altitude, and/or current heading of navigation unit 400 or an object to which navigation unit 400 is attached, among other navigation data. Inertial data 431 may also include historical data, such as initial or starting positions, past speeds and corresponding headings, past altitudes, and/or other navigational data.

Phase shift curve data 433 represents one or more stored sets of hyperbolic curves between two guided surface wave waveguide probes P. The phase shift curve data 433 represents those points between and around the corresponding two guided surface wave waveguide probes P, where the two guided waves emitted by the two guided surface wave waveguide probes P The phase difference between surface waves is equal to a certain value. Depending on the distance between two guided surface wave waveguide probes P, there may be multiple phase shift curve data 433 for a certain phase difference, since the guided surface waves traverse a distance equal to some multiple of their corresponding wavelength.

The multilateration application 423 is executed to identify the location of the navigation unit 400 based on one or more guided surface waves received by the navigation unit 400 . In some embodiments, the multilateration application 423 may calculate the position of the navigation unit 400 based, for example, on the length of time it takes for one or more guided surface waves to propagate from one or more corresponding guided surface wave waveguide probes P, as This article will discuss further. In various embodiments, the multilateration application 423 may, for example, be based on the signal strength of one or more guided surface waves measured at the location of the navigation unit 400 relative to the signal strength at one or more corresponding guided surface wave waveguide probes P. The difference between the respective signal strengths of one or more guided surface waves is used to calculate the position of the navigation unit 400, as will be discussed further herein. In various embodiments, the multilateration application 423 may also calculate the position of the navigation unit 400, for example, based on the phase shift between two or more guided surface waves measured at the position of the navigation unit 400, as will be described herein for further discussion. In one or more of these various embodiments, the multilateration application 423 may utilize additional data, such as map data 429, phase shift curves 433, inertial data 431, and/or other navigation data.

It should be understood that there may be other applications stored in the memory 416 and executable by the processor 430, as can be appreciated. These other applications may eg be performed to determine the strength of guided surface waves detected by the navigation unit 400 with the receiver 403 . Where any of the components discussed herein are implemented in software, a variety of programming languages can be employed such as, for example, C, C++, C#, Objective C, Perl, PHP, Visual Ruby, or other programming languages.

A number of software components are stored in memory 416 and are executable by processor 413 . In this regard, the term "executable" refers to a program file in a form that is ultimately executable by the processor 413 . An example of an executable program may be, for example, a compiled program that may be converted into machine code in a format that may be loaded into a random-access portion of memory 416 and executed by processor 413; may be represented as source code in a suitable format , such as object code that can be loaded into a random access portion of memory 416 and executed by processor 413; or may be interpreted by another executable program to generate instructions in a random access portion of memory 416 to be executed by processor 413 Executed source code, etc. The executable program may be stored in any portion or component of memory 416 including, for example, random access memory (RAM), read only memory (ROM), hard drive, solid state drive, USB flash drive, memory card, such as a compact disk (CD ) or a digital versatile disc (DVD) optical disc, floppy disc, magnetic tape or other memory component.

Memory 416 is defined herein to include both volatile and non-volatile memory and data storage components. Volatile components are components that do not retain data values when power is lost. Nonvolatile components are components that retain data when power is lost. Thus, memory 416 may include, for example, random access memory (RAM), read only memory (ROM), hard drives, solid state drives, USB flash drives, memory cards accessed through a memory card reader, accessed via an associated floppy disk drive, floppy disks, optical disks accessed via an optical drive, magnetic tapes accessed via an appropriate tape drive, and/or other storage components, or a combination of any two or more of these storage components. Additionally, RAM may include, for example, static random access memory (SRAM), dynamic random access memory (DRAM), or magnetic random access memory (MRAM), among other such devices. ROM may include, for example, Programmable Read Only Memory (PROM), Erasable Programmable Read Only Memory (EPROM), Electrically Erasable Programmable Read Only Memory (EEPROM), or other similar memory devices.

Furthermore, the processor 413 may represent a plurality of processors 413 and/or a plurality of processor cores, and the memory 416 may represent a plurality of memories 416 respectively operating in parallel processing circuits. In such a case, local interface 419 may be a suitable network that facilitates communication between any two of number of processors 413, between any processor 413 and any memory 416, or between any two memories 416, and so on. Local interface 419 may include additional systems designed to coordinate this communication, including, for example, performing load balancing. Processor 413 may be electrical or some other available structure.

While the multilateration application 423, as well as the various other systems described herein, may be implemented in software or code executed by general-purpose hardware as described above, it may alternatively be implemented on dedicated hardware or a combination of software/general-purpose and dedicated hardware. to fulfill. If embodied in dedicated hardware, each may be implemented as a circuit or a state machine employing any one or combination of various technologies. These techniques may include, but are not limited to, discrete logic circuits with logic gates for implementing various logic functions upon application of one or more data signals, application specific integrated circuits (ASICs) with appropriate logic gates, field programmable gate arrays ( FPGA) or other components, etc. Such techniques are generally known to those skilled in the art and thus are not described in detail herein.

With continued reference to FIG. 22 , a graphical representation of the location of the navigation unit 400 ( FIG. 21 ) determined by the multilateration application 423 ( FIG. 21 ) is shown. Here, the three ground stations 500 use their respective guided surface wave waveguide probes P to transmit guided surface waves. The navigation unit 400 receives each guided surface wave, and then the multilateration application 423 identifies the distance to each ground station 500, for example by determining the travel time of the guided surface wave from the ground station 500 or measuring the distance between the navigation unit 400 and the ground station 500. The variation of the signal strength of the guided surface wave between. The multilateration application 423 can then calculate a circle 503 around each ground station 500 . In other embodiments, the appropriate circumference 503 may be pre-calculated, and the multilateration application 423 may instead refer to the circumference 503 stored in the memory 416 of the navigation unit 400 (FIG. 21). For example, circumference 503 may be included in map data 429 ( FIG. 21 ) in data store 426 ( FIG. 21 ) of navigation unit 400 . Since the propagation velocity of guided surface waves emitted by ground stations 500 may vary based on the properties of the ground medium through which the guided surface waves pass, multilateration application 423 may need to adjust circumference 503 around each ground station accordingly. For example, a circle can become misshapen when surface waves are guided to travel. The multilateration application 423 may then identify locations 506 where a circle 503 around each ground station 500 intersects every other circle 503 around every other ground station 500 . This location 506 corresponds to the location 506 of the navigation unit 400 .

Some embodiments may use more than three ground stations 500 to achieve greater accuracy. For example, measurements of guided surface waves or data transmitted by guided surface waves may be inaccurate due to small differences in the accuracy of the time keeping mechanism at ground station 500 or interference with guided surface waves emitted from ground station 500 . The use of additional ground stations 500 allows identification and correction of errors and more accurate calculations of the multilateration application 423 . Other embodiments may use two ground stations 500 to identify two possible positions of the navigation unit 400, and use additional data and/or techniques, such as inertial data 431 (FIG. 21 ) and dead reckoning or other inertial navigation techniques, to One of the two potential locations 506 for the navigation unit 400 is eliminated.

Additionally, according to various embodiments of the present disclosure, ground station 500 may be configured in a master-slave configuration. In such an embodiment, the first ground station 500 transmits a first guided surface wave. Other ground stations 500 receive the first guided surface wave and transmit the guided surface wave in response. The other ground stations 500 may also wait for a predetermined period of time before transmitting the guided surface wave in response to receiving the first guided surface wave from the first ground station 500 . In such a configuration, the navigation unit 400 is able to identify the distance between the navigation unit 400 and each ground station 500 based on the time delay of arrival of each guided surface wave, as will be discussed in further detail herein. Furthermore, this configuration has the advantage of being self-synchronizing. Instead of having to keep the clocks at each ground station 500 synchronized in time to reliably transmit guided surface waves, only the clock at the first ground station 500 must be maintained because the timing of the transmission of guided surface waves by the remaining ground stations 500 is when the first A function of when the guided surface wave is received by each of the remaining ground stations 500 .

Applicant also notes that in embodiments relying on measurements of the strength of guided surface waves, standing or continuous waves may be used, since in these embodiments the time of arrival of guided surface waves is not necessary to identify navigational units 400's position 506. In such an embodiment, the use of standing or continuously guided surface waves allows the position 506 of the navigation unit 400 to be determined at any time. In contrast, embodiments that rely on calculating the distance from the navigation unit 400 to the ground station 500 require the navigation unit 400 to wait to receive guided surface waves emitted by a guided surface wave waveguide probe P located at the ground station.

Continuing reference to FIG. 23 , which shows phase shift curve data 433 used by the multilateration application 423 ( FIG. 21 ) to determine the position of the navigation unit 400 ( FIG. 21 ) using the phase difference of the guided surface waves measured by the navigation unit 400 graphical representation of . In such an embodiment, a pair of ground stations 500 (FIG. 22) each transmit a pair of phase-locked guided surface waves. Thus, the phase of each guided surface wave at a given location is a function of the number of wavelengths of the guided surface wave that traverse between ground station 500 and that location. For any individual phase shift curve 603 , the phase difference between the guided surface waves emitted by the two ground stations 500 is constant at any point along the phase shift curve 603 .

Because the phase of a guided surface wave cycles as it travels, there may be multiple phase shift curves 603 corresponding to a given phase difference between two guided surface waves emitted by two ground stations 500 . For example, for a phase difference of π/2 between two ground stations 500 , there may be multiple phase shift curves 603 . In order to identify the position 606 of the navigation unit 400, the difference in phase shift of the guided surface waves emitted by the second set of ground stations 500 may be measured. A phase shift curve 603 where the measured phase shifts of each set of ground stations 500 intersect represents a potential position 606 of the navigation unit 400 . Additional pairs of ground stations 500 and corresponding phase shift curves 603 may be used to further eliminate possible positions 606 in order to identify the actual position 606 of the navigation unit 400 . In some embodiments, additional data and/or techniques such as inertial data 431 ( FIG. 21 ) and dead reckoning or other inertial navigation techniques may be used to eliminate one or more potential locations 606 of navigation unit 400 in order to accurately The actual location of the navigation unit 400 is identified 606 .

The applicant also notes that measuring the phase difference between two or more guided surface waves at the location of the navigation unit 400 allows the use of standing or continuous guided surface waves, since measuring the arrival time of guided surface waves is not necessary of. In such an embodiment, multiple ground stations 500 may be involved, with each ground station transmitting a standing or continuous guided surface wave at a corresponding predetermined frequency unique to the ground station 500 . This can be achieved because if two ground stations 500 transmit guided surface waves at the same phase-locked frequency, the guided surface waves may be indistinguishable when detected by the navigation unit 400 . In some embodiments, each of ground stations 500 may transmit its respective standing or continuous guided surface wave at a harmonic or dominant frequency of some predefined baseline.

Referring to FIG. 24 , a depiction of a transport packet 700 that may be transmitted via guided surface waves is shown, according to various embodiments of the present disclosure. Transmission packet 700 may include timestamp 703 , station location 706 , initial signal strength 709 and/or initial phase offset 713 . Transport packet 700 can be used to send information to navigation unit 400 ( FIG. 21 ) so that multilateration application 423 ( FIG. 21 ) can accurately identify the location of navigation unit 400 . By sending the information in transport packets 700, the navigation unit 400 does not have to store the information locally in the memory 416 (FIG. 21) or in the data store 426 of the navigation unit 400 (FIG. 21). Additionally, any internal clocks or timing devices of the navigation unit 400 may be kept synchronized with the clocks of the ground stations emitting the guided surface waves. Furthermore, in those embodiments that measure the time delay in arrival of the guided surface wave or measure the time it takes for the guided surface wave to travel from the ground station 500 ( FIG. 22 ) to the location 506 of the navigation unit 400 ( FIG. 22 ), the transmission Grouping allows the use of standing or continuously guided surface waves. In such an embodiment, the time of arrival of the transport packet 700 carried by the guided surface waves may be used instead of the guided surface waves themselves. However, transport packet 700 may be sent with any of the embodiments described herein using amplitude modulation, frequency modulation, and/or other techniques.

Timestamp 703 identifies the time when transport packet 700 was created or when the transport packet was sent via guided surface waves. In embodiments where the timestamp 703 represents the time at which the transport packet 700 was created, a previously defined delay may exist between the creation of the transport packet 700 and the sending of the transport packet 700 such that the time at which the transport packet 700 is sent with the guided surface waves may Determined by adding or subtracting a delay from the timestamp 703 depending on how the timestamp 703 is formatted. The navigation unit 400 may determine the distance between the navigation unit 400 and the ground station 500 that sent the transmission packet based on the timestamp 703 using the following formula:

Distance＝Speed _Wave (Time _Received -Time _Send )

The variable Speed _Wave is the known speed at which surface waves are guided to travel across the Earth's surface, the variable Time _Received is the time when the transmission packet 700 was received by the navigation unit 400, and the variable Time _Send represents the value of the time stamp 703 of the transmission packet 700.

Station location 706 represents the geographic coordinates of ground station 500 (FIG. 22) from which transmission packet 700 was transmitted. Based on the station location 706 and the distance to the station location 706 calculated based on the time stamp 703, as described above, the navigation unit 400 can identify a circle around the ground station 500, wherein the circle has a center equal to the station location 706 and equal to the calculated distance The radius of , as described above.

The initial signal strength 709 represents the signal strength of the guided surface wave when transmitted by the guided surface wave waveguide probe P at the ground station 500 . Because guided surface waves lose strength as a function of the distance between the guided surface wave waveguide probe P at the ground station 500 and the position 506 of the navigation unit 400, the navigation unit 400 can compare the initial signal strength measured by the navigation unit 400 by calculating 709 The distance between the location 506 of the navigation unit 400 and the ground station 506 is calculated as the difference between the signal strengths of the navigation unit 400 and the ground station 506 .

However, in embodiments with a limited number of ground stations 500 , the strength of each guided surface wave at each ground station may be a known quantity stored in the memory 416 of the navigation unit 400 . In such embodiments, initial signal strength 709 may be omitted from transmission packet 700, or may be used to synchronize navigation unit 400 with current conditions.

Phase offset 713 represents the initial phase of the guided surface wave carrying transport packet 700 . Phase offset 713 may be used by those embodiments that identify the location of navigation unit 400 based on the phase difference of a plurality of guided surface waves at location 606 ( FIG. 23 ) of navigation unit 400 . In such an embodiment, transmitting the phase offset 713 allows the navigation unit 400 to remain synchronized with the ground station 500 .

Referring now to FIG. 25 , a flowchart providing one example of the operation of a portion of the multilateration application 423 according to various embodiments is shown. It will be appreciated that the flowchart of FIG. 25 merely provides an example of many different types of functional arrangements that may be used to effectuate the operation of a portion of the multilateration application 423 as described herein. Alternatively, the flowchart of FIG. 25 may be considered an example depicting elements of a method implemented in computing device 409 ( FIG. 21 ) in accordance with one or more embodiments.

Beginning at block 803, the multilateration application 423 determines whether a minimum number of guided surface wave waveguide probes P are available for geolocation. The multilateration application 423 can determine this by determining the number of guided surface waves detected by the navigation unit 400 (FIG. 21). Each guided surface wave may eg correspond to a guided surface wave waveguide probe P at ground station 500 ( FIG. 22 ). Accordingly, the multilateration application 423 may determine whether a minimum number of ground stations 500 are available by counting the number of guided surface waves detectable by the navigation unit 400 . If a minimum number of guided surface wave waveguide probes P are available, execution proceeds to block 806 . Otherwise, execution ends.

Continuing to block 806 , the multilateration application 423 identifies which transmission corresponds to which ground station 500 . For example, each ground station 500 may be associated with a guided surface wave tuned to a particular frequency. By identifying the frequency of the guided surface wave, the multilateration application 423 can determine which ground station 500 has the guided surface wave waveguide probe P that emits the guided surface wave.

Continuing to block 809, in various embodiments, the multilateration application 423 may parse the data in the transport packet 700 (FIG. 24) carried by the guided surface waves. For example, the multilateration application 423 may use the information contained in the transmission packet 700 to determine the time of the guided surface wave transmission, the location of the ground station 500 and the guided surface wave waveguide probe P that emitted the guided surface wave, and/or potentially include Other data in transport packet 700.

Referring next to block 813 , the multilateration application 423 calculates the distance from the navigation unit 400 to each ground station 500 . The navigation unit 400 can determine the distance between the navigation unit 400 and the ground station 500 that sent the transmission packet based on the time stamp 703 ( FIG. 24 ) of the transmission packet 700 using the following formula:

Distance＝Speed _Wave (Time _Received -Time _Send )

Where the variable Speed _Wave is the known speed at which surface waves are guided to travel across the Earth's surface, the variable Time _Received is the time when the transmission packet 700 was received by the navigation unit 400, and the variable Time _Send represents the value in the timestamp 703 of the transmission packet 700.

Proceeding next to block 816 , the multilateration application 423 calculates, plots, or otherwise generates a circle around each ground station 500 used to identify the location 506 ( FIG. 22 ) of the navigation unit 400 . The circumference may be calculated, for example, by creating a circle with a center equal to the location of the ground station 500 and a radius equal to the calculated distance to the location of the ground station, as described above. The location of the ground station 500 may be known in advance and stored in the memory 416 of the navigation device 400 ( FIG. 21 ), or may be determined based on the station location 706 parsed from the transmission packet 700 ( FIG. 24 ).

Moving to block 819, the multilateration application 423 identifies locations 506 where each circle intersects every other circle. This intersection represents the position 506 of the navigation unit 400 relative to each ground station 500 involved. Execution then ends.

Referring now to FIG. 26 , a flowchart illustrating one example of the operation of providing a portion of the multilateration application 423 is shown, in accordance with various embodiments. It will be appreciated that the flowchart of FIG. 26 provides only an example of many different types of functional arrangements that may be used to effectuate the operation of a portion of the multilateration application 423 as described herein. Alternatively, the flowchart of FIG. 26 may be considered an example depicting elements of a method implemented in computing device 409 ( FIG. 21 ) in accordance with one or more embodiments.

Beginning at block 903, the multilateration application 423 determines whether a minimum number of guided surface wave waveguide probes P are available for geolocation. The multilateration application 423 can determine this by determining the number of guided surface waves detected by the navigation unit 400 (FIG. 21). Each guided surface wave may eg correspond to a guided surface wave waveguide probe P at ground station 500 ( FIG. 22 ). Accordingly, the multilateration application 423 may determine whether a minimum number of ground stations 500 are available by counting the number of guided surface waves detectable by the navigation unit 400 . If a minimum number of guided surface wave waveguide probes P are available, execution proceeds to block 906 . Otherwise, execution ends.

Proceeding next to block 906 , the multilateration application 423 identifies which transmission corresponds to which ground station 500 . For example, each ground station 500 may be associated with a guided surface wave tuned to a particular frequency. By identifying the frequency of the guided surface wave, the multilateration application 423 can determine which ground station 500 has the guided surface wave waveguide probe P that emits the guided surface wave.

Moving to block 909 , the multilateration application 423 determines the strength of each guided surface wave detected by the navigation unit 400 at the location 506 of the navigation unit 400 . Intensity may be measured by the navigation unit 400 using the receiver 403 of the navigation unit 400 (FIG. 21) and corresponding circuitry, sensors or applications.

Referring next to block 913, the distance to each ground station 500 is determined. Each guided surface wave emitted from the guided surface waveguide probe P at the ground station 500 will have an initial intensity. As the guided surface wave travels from the ground station 500, the intensity will decrease in a predictable manner. In the case of a guided surface wave passing through a sphere, the intensity will decrease due to geometrical diffusion as the guided surface wave travels towards the equator relative to the position of the ground station 500, and then converges to a point as the guided surface wave continues to travel towards the antipodes The intensity increases again. The multilateration application 423 can determine the distance of the navigation unit 400 from each ground station by determining the change in the strength of the guided surface waves between the ground station 500 and the navigation unit 400 . In some embodiments, the strength of the guided surface wave when transmitted at the ground station may be previously known and stored in the memory 416 of the navigation unit 400 . In other embodiments, guided surface waves may be used as the carrier for transmission packet 700 (FIG. 24), which includes an initial signal strength 709 representing the strength of the guided surface waves at the time of transmission.

Proceeding to block 916 , the multilateration application 423 calculates, plots, or otherwise generates a circle around each ground station 500 used to identify the location 506 ( FIG. 22 ) of the navigation unit 400 . The circumference may be calculated, for example, by creating a circle with a center equal to the location of the ground station 500 and a radius equal to the calculated distance to the location of the ground station, as described above. The location of the ground station 500 may be known in advance and stored in the memory 416 of the navigation device 400 ( FIG. 21 ), or may be determined based on the station location 706 parsed from the transmission packet 700 ( FIG. 24 ).

Moving to block 919, the multilateration application 423 identifies locations 506 where each circle intersects every other circle. This intersection represents the potential position 506 of the navigation unit 400 relative to each of the ground stations 500 involved. In some embodiments, there may be only one intersection corresponding to the position 506 of the navigation unit 400 where the guided wave travels a short distance. In embodiments where guided waves travel longer distances, such as guided surface waves traversing an entire sphere, multiple potential locations 506 can be identified because each guided surface wave has a given intensity in a hemisphere centered at originating ground station 500 and a second set of positions of the same intensity in the hemisphere centered on the antipode of the ground station 500, for reasons discussed earlier.

Referring next to block 923 , the current location is identified based on intersections previously determined in block 919 . For those embodiments using guided surface waves traveling short or medium distances, the multilateration application 423 determines a single common intersection as the location 506 of the navigation unit 400 . For those embodiments using guided surface waves traveling medium to long distances, such as guided surface waves traversing the entire earth, the multilateration application 423 may utilize additional data to identify the actual location 506 from the set of potential locations 506 . For example, the multilateration application 423 may use the inertial data 431 stored by the navigation unit 400 to determine that the navigation unit 400 is located in the Northern Hemisphere or the North American continent, and thus identify a location 506 on the Northern Hemisphere or North American continent as the location 506 of the navigation unit 400. Execution then ends.

Reference is next made to FIG. 27 , which shows a flowchart providing one example of the operation of a portion of the multilateration application 423 in accordance with various embodiments. It will be appreciated that the flowchart of FIG. 27 provides only an example of many different types of functional arrangements that may be used to effectuate the operation of a portion of the multilateration application 423 as described herein. Alternatively, the flowchart of FIG. 27 may be considered an example depicting elements of a method implemented in computing device 409 ( FIG. 21 ) in accordance with one or more embodiments.

Beginning at block 1003, the multilateration application 423 determines whether a minimum number of guided surface wave waveguide probes P are available for geolocation. The multilateration application 423 can determine this by determining the number of guided surface waves detected by the navigation unit 400 (FIG. 21). Each guided surface wave may eg correspond to a guided surface wave waveguide probe P at ground station 500 ( FIG. 22 ). Accordingly, the multilateration application 423 may determine whether a minimum number of ground stations 500 are available by counting the number of guided surface waves detectable by the navigation unit 400 . If a minimum number of guided surface wave waveguide probes P are available, execution proceeds to block 1006 . Otherwise, execution ends.

Proceeding to block 1006 , the multilateration application 423 identifies which transmission corresponds to which ground station 500 . For example, each ground station 500 may be associated with a guided surface wave tuned to a particular frequency, such as a harmonic of the fundamental frequency. By identifying the frequency of the guided surface wave, the multilateration application 423 can determine which ground station 500 corresponds to the guided surface wave waveguide probe P that emitted the guided surface wave.

Moving to block 1009 , the multilateration application 423 determines the phase difference between the two guided surface waves from the two ground stations 500 detected by the navigation unit 400 at the location 606 of the navigation unit 400 ( FIG. 23 ). The phase difference may be measured by the navigation unit 400 using the receiver 403 of the navigation unit 400 (FIG. 21) and corresponding circuitry, sensors or applications. The multilateration application 423 performs this function for each pair of ground stations 500 used to fix the position of the navigation unit 400 .

Referring next to block 1013, the multilateration application 423 identifies a set of phase shift curves 603 (FIG. 23). Each phase shift curve represents a continuous set of points between two ground stations 500 where the phase-locked guided surface waves from the ground stations 500 differ from the detected phase shift. Since the phase of each guided surface wave cycles periodically as each guided surface wave traverses its wavelength, multiple phase shift curves for a given phase difference may exist between the pair of ground stations 500 . Accordingly, the set of phase shift curves 603 may include a plurality of phase shift curves 603 .

Proceeding next to block 1016 , the multilateration application 423 identifies where each set of phase shift curves 433 intersects each other set of phase shift curves 603 . The locations 606 where groups of phase shift curves 603 intersect correspond to possible locations 606 of the navigation unit 400 . Due to the periodicity of the phase of the guided surface waves, each set of phase shift curves 603 may intersect every other set of phase shift curves 603 at multiple locations 606 .

Moving to block 1019 , the multilateration application 423 identifies the intersection of the set of phase shift curves 603 corresponding to the position of the navigation unit 400 . The multilateration application 423 may utilize additional data, such as inertial data 431 (FIG. 21), for identification. For example, if the multilateration application 423 determines that the navigation unit 400 is located in the United States, the multilateration application 423 will only select the intersection of the phase shift curve 603 corresponding to a location 606 within the United States. The flowcharts of FIGS. 25 , 26 and 27 illustrate the functionality and operation of the implementation of portions of the multilateration application 423 . If implemented as software, each block may represent a module, segment or code portion(s) that includes program instructions for implementing the specified logical function. Program instructions may be implemented in the form of source code, which includes human readable statements written in a programming language, or machine code including instructions that can be executed by a suitable execution system, such as processor 413 (FIG. 21 ) in a computer system or other system) recognized digital commands. Machine code can be converted from source code etc. If embodied as hardware, each block may represent a circuit or multiple interconnected circuits to carry out the specified logical function.

The flowcharts of Figures 25, 26, and 27 show a particular order of execution, but it should be understood that the order of execution may differ from that shown. For example, the order of execution of two or more blocks may be scrambled relative to the order shown. Furthermore, two or more blocks shown in succession in Figures 25, 26 and 27 may be executed concurrently or with partial concurrence. Additionally, in some embodiments, one or more of the blocks shown in Figures 25, 26, and 27 may be skipped or omitted. Additionally, any number of counters, state variables, warning signals, or messages may be added to the logic flows described herein for purposes of enhancing usability, billing, performance measurement, or providing troubleshooting assistance, among others. It should be understood that all such variations are within the scope of this disclosure.

Additionally, any logic or applications described herein, including the multilateration application 423, including software or code, may be embodied on any non-transitory computer-readable medium for use by or with a processor such as, for example, a computer system or other system 413 instruction execution system to use. In this sense, logic may include, for example, statements, including instructions and statements, that may be read from a computer-readable medium and executed by an instruction execution system. In the context of this disclosure, a "computer-readable medium" may be any medium that can contain, store or maintain the logic or applications described herein for use by or in connection with the instruction execution system.

Computer readable media may include any of many physical media, such as magnetic media, optical media, or semiconductor media. More specific examples of suitable computer readable media would include, but are not limited to, magnetic tapes, magnetic floppy diskettes, magnetic hard drives, memory cards, solid state drives, USB flash drives, or optical disks. Also, the computer readable medium may be random access memory (RAM) including, for example, static random access memory (SRAM) and dynamic random access memory (DRAM), or magnetic random access memory (MRAM). Furthermore, the computer readable medium can be a read only memory (ROM), programmable read only memory (PROM), erasable programmable read only memory (EPROM), electrically erasable programmable read only memory (EEPROM)) or Other types of memory devices.

Furthermore, any of the logic or applications described herein, including the multilateration application 423, can be implemented and structured in various ways. For example, one or more applications described may be implemented as modules or components of a single application. Furthermore, it should be understood that terms such as "application," "service," "system," "engine," "module," etc. may be interchangeable and are not intended to be limiting.

Disjunctive language such as the phrase "at least one of X, Y, or Z", as understood in the context of its usual use unless otherwise stated, to denote an item, term, etc., may be X, Y, or Z, or Any combination (eg, X, Y, and/or Z). Thus, such disjunctive language generally does not intend and should not imply the presence of at least one of X, at least one of Y, or at least one of Z to each that certain embodiments require.

It should be emphasized that the above-described embodiments of the present disclosure are merely possible examples of implementations set forth for a clear understanding of the principles of the disclosure. Many variations and modifications can be made to the above-described embodiments without departing substantially from the spirit and principles of this disclosure. All such modifications and variations are intended to be included within the scope of this disclosure and protected by the appended claims. Furthermore, all optional and preferred features and modifications of the described embodiments and the dependent claims are applicable to all aspects of the disclosure taught herein. Furthermore, the individual features of the dependent claims as well as all optional and preferred features and modifications of the described embodiments are combinable and interchangeable with each other.

Claims (20)

1. A system comprising: A first guided surface waveguide probe comprising a first charging terminal raised above a first lossy conducting medium configured to generate a composite waveguide incident at a first complex Brewster incidence angle (θ _i,B ) of said first lossy conducting medium At least one recombination field before the first wave of ; circuitry communicatively coupled to the first guided surface waveguide probe, wherein the circuitry coupled to the first guided surface waveguide probe is configured to transmit the first guided surface waveguide probe at least at a first frequency via the first guided surface waveguide probe Wave; A second guided surface waveguide probe, including a second charging terminal raised above the second lossy conducting medium _, is configured to produce a second at least one recombination field of the wavefront; circuitry communicatively coupled to the second guided surface waveguide probe, wherein the circuitry communicatively coupled to the second guided surface waveguide probe is configured to transmit via the second guided surface waveguide probe at least at a second frequency a second guided surface wave; A third guided surface waveguide probe, including a third charging terminal raised above the third lossy conducting medium, is configured to generate a second complex Brewster incidence angle (θ _i,B ) of the third lossy conducting medium at least one composite field of three wavefronts; and circuitry communicatively coupled to the third guided surface waveguide probe, wherein the circuitry communicatively coupled to the third guided surface waveguide probe is configured to transmit via the third guided surface waveguide probe at least at a third frequency The third guides surface waves. 2. The system of claim 1 , further comprising a first guided surface wave receiving structure and a second guided surface wave receiving structure configured to receive signals from the The first guided surface wave obtains electrical energy, and the second guided surface wave receiving structure is configured to obtain electrical energy from the second guided surface wave traveling along the ground medium, wherein The circuitry communicatively coupled to the second guided surface waveguide probe is also communicatively coupled to the first guided surface wave receiving structure, and the circuitry communicatively coupled to the second guided surface waveguide probe is configured to at least: determining that the first guided surface wave is received by the first guided surface wave receiving structure; and transmitting the second guided surface wave at the second frequency via the second guided surface waveguide probe in response to a determination that the first guided surface wave is received by the first guided surface wave receiving structure; The circuitry communicatively coupled to the third guided surface waveguide probe is further communicatively coupled to the second guided surface wave receiving structure, and the circuitry communicatively coupled to the third guided surface waveguide probe is configured to at least: determining that the first guided surface wave is received by the second guided surface wave receiving structure; and In response to determining that the first guided surface wave is received by the second guided surface wave receiving structure, transmitting the third guided surface wave at the third frequency via the third guided surface waveguide probe. 3. The system of any one of claims 1-2, wherein the second guided surface wave is a predefined time period after the first guided surface wave is received by the first guided surface wave receiver emission. 4. The system of any one of claims 1-3, wherein the third guided surface wave is a predefined time period after the first guided surface wave is received by the first guided surface wave receiver emission. 5. The system of any one of claims 1-4, wherein at least one of the first guided surface wave, the second guided surface wave, or the third guided surface wave includes a carrier. 6. The system according to any one of claims 1-5, wherein said data comprises transport packets comprising: timestamp; and The location of at least one of the first guided surface wave waveguide probe, the second guided surface wave waveguide probe or the third guided surface wave waveguide probe. 7. The system according to any one of claims 1-6, further comprising a feed network electrically coupled to said first charging terminal, said feed network providing a phase delay (Φ ), the wave tilt angle is related to the complex Brewster incidence angle (θ _i,B ) associated with the lossy conducting medium near the first guiding surface waveguide probe. 8. A method comprising: transmitting a first guided surface wave at a first frequency via a first guided surface wave probe; transmitting a second guided surface wave at a second frequency via a second guided surface wave probe, wherein the second guided surface wave is phase locked to the first guided surface wave; and A third guided surface wave is transmitted at a third frequency via a third guided surface wave probe, wherein the third guided surface wave is phase locked to the first guided surface wave. 9. The method of claim 8, wherein the first frequency, the second frequency and the third frequency are harmonics of a fundamental frequency. 10. The method of any one of claims 8-9, wherein the second frequency and the third frequency are harmonics of the first frequency. 11. A method according to any one of claims 8-10, wherein said first guided surface wave comprises a continuously generated wave. 12. A method according to any one of claims 8-11, wherein said second guided surface wave comprises a continuously generated wave. 13. A method according to any one of claims 8-12, wherein said third guided surface wave comprises continuously generated. 14. The method of any one of claims 8-13, wherein at least one of the first guided surface wave, the second guided surface wave or the third guided surface wave is amplitude modulated to carry a transmission packet , the transmission packet includes an initial phase of the first guided surface wave. 15. A device comprising: a guided surface wave receiving structure configured to obtain electrical power from guided surface waves traveling along the ground medium; an electrical load coupled to the guided surface wave receiving structure as a load coupled to an excitation source of a guided surface wave waveguide probe generating the guided surface wave; processor; memory; and An application comprising a set of instructions stored in the memory which, when executed by the processor, causes the processor to: calculating the distance traveled by the guided surface wave from the guided surface wave waveguide probe to the location of the guided surface wave receiving structure; and A set of coordinates for the location is determined based at least in part on a distance traveled by the guided surface wave from the guided surface wave waveguide probe to the guided surface wave receiving structure. 16. The apparatus of claim 15, wherein the guided surface wave receiving structure is selected from the group consisting of a linear probe, a tuned resonator, and a coil. 17. The apparatus of any one of claims 15-16, wherein the guided surface wave receiving structure is configured to receive guided surface waves at a plurality of different frequencies substantially simultaneously. 18. The apparatus of any one of claims 15-17, wherein causing the processor to calculate the distance traveled by the guided surface wave to the location of the apparatus further comprises causing the processor to at least: determining a first intensity of the guided surface wave corresponding to an initial intensity of the guided surface wave of the guided surface wave waveguide probe; determining a second intensity of the guided surface wave corresponding to the intensity of the guided surface wave at the location of the device; calculating a change in intensity between said first intensity and said second intensity; and A distance traveled by the guided surface wave is calculated based at least in part on the change in intensity. 19. The apparatus of any one of claims 15-18, wherein causing the processor to calculate the distance traveled by the guided surface wave further comprises causing the processor to at least: determining a launch time of the guided surface wave from the guided surface wave waveguide probe; determining a time of arrival of the guided surface wave at the device; calculating a time difference between said launch time and said arrival time to generate a travel time for said guided surface wave; and The distance traveled by the guided surface wave is calculated based at least in part on the travel time of the guided surface wave. 20. The apparatus according to any one of claims 19-20, wherein the emission time of the guided surface wave is encoded in the guided surface wave.